Lozano-Robledo, Álvaro A probabilistic model for the distribution of ranks of elliptic curves over \(\mathbb{Q}\). (English) Zbl 07300435 J. Number Theory 221, 270-338 (2021). MSC: 11G05 14H52 PDF BibTeX XML Cite \textit{Á. Lozano-Robledo}, J. Number Theory 221, 270--338 (2021; Zbl 07300435) Full Text: DOI
Lim, Meng Fai On the control theorem for fine Selmer groups and the growth of fine Tate-Shafarevich groups in \(\mathbb{Z}_p\)-extensions. (English) Zbl 07304472 Doc. Math. 25, 2445-2471 (2020). MSC: 11R23 11G05 11S25 PDF BibTeX XML Cite \textit{M. F. Lim}, Doc. Math. 25, 2445--2471 (2020; Zbl 07304472) Full Text: DOI
Kundu, Debanjana Growth of fine Selmer groups in infinite towers. (English) Zbl 07303622 Can. Math. Bull. 63, No. 4, 921-936 (2020). MSC: 11R23 PDF BibTeX XML Cite \textit{D. Kundu}, Can. Math. Bull. 63, No. 4, 921--936 (2020; Zbl 07303622) Full Text: DOI
Liu, Yifeng; Tian, Yichao Supersingular locus of Hilbert modular varieties, arithmetic level raising and Selmer groups. (English) Zbl 07275222 Algebra Number Theory 14, No. 8, 2059-2119 (2020). MSC: 14G35 11G05 11R34 PDF BibTeX XML Cite \textit{Y. Liu} and \textit{Y. Tian}, Algebra Number Theory 14, No. 8, 2059--2119 (2020; Zbl 07275222) Full Text: DOI
Bhargava, M.; Shankar, A.; Taniguchi, T.; Thorne, F.; Tsimerman, J.; Zhao, Y. Bounds on 2-torsion in class groups of number fields and integral points on elliptic curves. (English) Zbl 07268738 J. Am. Math. Soc. 33, No. 4, 1087-1099 (2020). Reviewer: Sajad Salami (Rio de Janeiro) MSC: 11G05 11R29 PDF BibTeX XML Cite \textit{M. Bhargava} et al., J. Am. Math. Soc. 33, No. 4, 1087--1099 (2020; Zbl 07268738) Full Text: DOI
Bandini, Andrea; Bars, Francesc; Longhi, Ignazio Aspects of Iwasawa theory over function fields. (English) Zbl 07242511 Böckle, Gebhard (ed.) et al., \(t\)-motives: Hodge structures, transcendence and other motivic aspects. Zürich: European Mathematical Society (EMS) (ISBN 978-3-03719-198-9/hbk; 978-3-03719-698-4/ebook). EMS Series of Congress Reports, 375-416 (2020). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11G09 11G05 11R58 11G40 PDF BibTeX XML Cite \textit{A. Bandini} et al., in: \(t\)-motives: Hodge structures, transcendence and other motivic aspects. Zürich: European Mathematical Society (EMS). 375--416 (2020; Zbl 07242511) Full Text: DOI
Burns, David On the Galois structure of arithmetic cohomology. I: Compactly supported \(p\)-adic cohomology. (English) Zbl 07236579 Nagoya Math. J. 239, 294-321 (2020). Reviewer: Piotr Krasoń (Szczecin) MSC: 11R34 11R23 20C11 PDF BibTeX XML Cite \textit{D. Burns}, Nagoya Math. J. 239, 294--321 (2020; Zbl 07236579) Full Text: DOI
Ohshita, Tatsuya Asymptotic lower bound of class numbers along a Galois representation. (English) Zbl 07185506 J. Number Theory 211, 95-112 (2020). Reviewer: Piotr Krasoń (Szczecin) MSC: 11R29 11G05 11G10 11R23 PDF BibTeX XML Cite \textit{T. Ohshita}, J. Number Theory 211, 95--112 (2020; Zbl 07185506) Full Text: DOI
Ahmed, Suman; Lim, Meng Fai On the Euler characteristics of signed Selmer groups. (English) Zbl 07184159 Bull. Aust. Math. Soc. 101, No. 2, 238-246 (2020). MSC: 11R23 11G05 11S25 PDF BibTeX XML Cite \textit{S. Ahmed} and \textit{M. F. Lim}, Bull. Aust. Math. Soc. 101, No. 2, 238--246 (2020; Zbl 07184159) Full Text: DOI
Gillibert, Jean; Gillibert, Pierre On the splitting of the Kummer exact sequence. (English) Zbl 1451.14081 Actes de la conférence \guillemotleft Analogies between number field and function field : algebraic and analytic approaches \guillemotright. Besançon: Presses Universitaires de Franche-Comté. Publ. Math. Besançon, Algèbre Théor. Nombres 2019, Part 2, 19-27 (2019). MSC: 14G40 18G10 14K15 11R29 20K10 PDF BibTeX XML Cite \textit{J. Gillibert} and \textit{P. Gillibert}, Publ. Math. Besançon, Algèbre Théor. Nombres 2019, 19--27 (2019; Zbl 1451.14081)
Bhargava, Manjul; Klagsbrun, Zev; Oliver, Robert J. Lemke; Shnidman, Ari \(3\)-isogeny Selmer groups and ranks of abelian varieties in quadratic twist families over a number field. (English) Zbl 1442.14084 Duke Math. J. 168, No. 15, 2951-2989 (2019). Reviewer: G. K. Sankaran (Bath) MSC: 14G05 11G10 PDF BibTeX XML Cite \textit{M. Bhargava} et al., Duke Math. J. 168, No. 15, 2951--2989 (2019; Zbl 1442.14084) Full Text: DOI Euclid
Yu, Myungjun The distribution of Selmer ranks of quadratic twists of Jacobians of hyperelliptic curves. (English) Zbl 07124456 Math. Res. Lett. 26, No. 4, 1217-1250 (2019). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G10 14D10 14G05 14G25 14K15 14H40 PDF BibTeX XML Cite \textit{M. Yu}, Math. Res. Lett. 26, No. 4, 1217--1250 (2019; Zbl 07124456) Full Text: DOI
Hatley, Jeffrey; Lei, Antonio Comparing anticyclotomic Selmer groups of positive co-ranks for congruent modular forms. (English) Zbl 07124451 Math. Res. Lett. 26, No. 4, 1115-1144 (2019). MSC: 11R23 14H52 PDF BibTeX XML Cite \textit{J. Hatley} and \textit{A. Lei}, Math. Res. Lett. 26, No. 4, 1115--1144 (2019; Zbl 07124451) Full Text: DOI arXiv
Longo, Matteo; Vigni, Stefano Plus/minus Heegner points and Iwasawa theory of elliptic curves at supersingular primes. (English) Zbl 1431.11123 Boll. Unione Mat. Ital. 12, No. 3, 315-347 (2019). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11G05 PDF BibTeX XML Cite \textit{M. Longo} and \textit{S. Vigni}, Boll. Unione Mat. Ital. 12, No. 3, 315--347 (2019; Zbl 1431.11123) Full Text: DOI arXiv
Thorne, Jack A. On the average number of 2-Selmer elements of elliptic curves over \(\mathbb F_q(X)\) with two marked points. (English) Zbl 07087907 Doc. Math. 24, 1179-1223 (2019). MSC: 11G05 14H60 PDF BibTeX XML Cite \textit{J. A. Thorne}, Doc. Math. 24, 1179--1223 (2019; Zbl 07087907) Full Text: DOI
Loeffler, David; Zerbes, Sarah Livia Iwasawa theory for the symmetric square of a modular form. (English) Zbl 1430.11149 J. Reine Angew. Math. 752, 179-210 (2019). Reviewer: Andrea Bandini (Pisa) MSC: 11R23 PDF BibTeX XML Cite \textit{D. Loeffler} and \textit{S. L. Zerbes}, J. Reine Angew. Math. 752, 179--210 (2019; Zbl 1430.11149) Full Text: DOI
Hatley, Jeffrey; Lei, Antonio Arithmetic properties of signed Selmer groups at non-ordinary primes. (Propriétés arithmétiques des groupes de Selmer signés pour les nombres premiers non-ordinaires.) (English. French summary) Zbl 07067431 Ann. Inst. Fourier 69, No. 3, 1259-1294 (2019). MSC: 11R18 11F11 11R23 11F85 PDF BibTeX XML Cite \textit{J. Hatley} and \textit{A. Lei}, Ann. Inst. Fourier 69, No. 3, 1259--1294 (2019; Zbl 07067431) Full Text: DOI arXiv
Palvannan, Bharathwaj Height one specializations of Selmer groups. (Spécialisations de hauteur un des groupes de Selmer.) (English. French summary) Zbl 1443.11228 Ann. Inst. Fourier 69, No. 1, 303-334 (2019). Reviewer: Andrea Bandini (Pisa) MSC: 11R23 11F33 11F80 PDF BibTeX XML Cite \textit{B. Palvannan}, Ann. Inst. Fourier 69, No. 1, 303--334 (2019; Zbl 1443.11228) Full Text: DOI arXiv
Masoero, Daniele On the structure of Selmer and Shafarevich-Tate groups of even weight modular forms. (English) Zbl 07062713 Trans. Am. Math. Soc. 371, No. 12, 8381-8404 (2019). MSC: 11F11 14C25 PDF BibTeX XML Cite \textit{D. Masoero}, Trans. Am. Math. Soc. 371, No. 12, 8381--8404 (2019; Zbl 07062713) Full Text: DOI
Morgan, Adam Quadratic twists of abelian varieties and disparity in Selmer ranks. (English) Zbl 07059758 Algebra Number Theory 13, No. 4, 839-899 (2019). Reviewer: Sajad Salami (Rio de Janeiro) MSC: 11G10 PDF BibTeX XML Cite \textit{A. Morgan}, Algebra Number Theory 13, No. 4, 839--899 (2019; Zbl 07059758) Full Text: DOI
Nichifor, Alexandra; Palvannan, Bharathwaj On free resolutions of Iwasawa modules. (English) Zbl 1425.11174 Doc. Math. 24, 609-662 (2019). Reviewer: Wei Feng (Beijing) MSC: 11R23 11R34 11S25 PDF BibTeX XML Cite \textit{A. Nichifor} and \textit{B. Palvannan}, Doc. Math. 24, 609--662 (2019; Zbl 1425.11174) Full Text: DOI arXiv
Li, Chao 2-Selmer groups, 2-class groups and rational points on elliptic curves. (English) Zbl 1448.11108 Trans. Am. Math. Soc. 371, No. 7, 4631-4653 (2019). MSC: 11G05 14G35 11G40 11F33 PDF BibTeX XML Cite \textit{C. Li}, Trans. Am. Math. Soc. 371, No. 7, 4631--4653 (2019; Zbl 1448.11108) Full Text: DOI
Yu, Myungjun Large Shafarevich-Tate groups over quadratic number fields. (English) Zbl 07030976 J. Number Theory 199, 98-109 (2019). MSC: 11G05 14G25 11G40 14G05 PDF BibTeX XML Cite \textit{M. Yu}, J. Number Theory 199, 98--109 (2019; Zbl 07030976) Full Text: DOI arXiv
Sakamoto, Ryotaro Stark systems over Gorenstein local rings. (English) Zbl 1425.11175 Algebra Number Theory 12, No. 10, 2295-2326 (2018). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11F80 11R34 PDF BibTeX XML Cite \textit{R. Sakamoto}, Algebra Number Theory 12, No. 10, 2295--2326 (2018; Zbl 1425.11175) Full Text: DOI
Dummit, David S.; Voight, John The 2-Selmer group of a number field and heuristics for narrow class groups and signature ranks of units. (English) Zbl 06968908 Proc. Lond. Math. Soc. (3) 117, No. 4, 682-726 (2018). MSC: 11R29 11R27 11R45 11Y40 PDF BibTeX XML Cite \textit{D. S. Dummit} and \textit{J. Voight}, Proc. Lond. Math. Soc. (3) 117, No. 4, 682--726 (2018; Zbl 06968908) Full Text: DOI
Kitajima, Takahiro; Otsuki, Rei On the plus and the minus Selmer groups for elliptic curves at supersingular primes. (English) Zbl 1411.11106 Tokyo J. Math. 41, No. 1, 273-303 (2018). Reviewer: Andrea Bandini (Pisa) MSC: 11R23 11G05 11G07 PDF BibTeX XML Cite \textit{T. Kitajima} and \textit{R. Otsuki}, Tokyo J. Math. 41, No. 1, 273--303 (2018; Zbl 1411.11106) Full Text: DOI arXiv
Burns, David On the Galois structure of arithmetic cohomology. III: Selmer groups of critical motives. (English) Zbl 1452.11074 Kyoto J. Math. 58, No. 3, 671-693 (2018). MSC: 11G35 11R33 11R34 PDF BibTeX XML Cite \textit{D. Burns}, Kyoto J. Math. 58, No. 3, 671--693 (2018; Zbl 1452.11074) Full Text: DOI
Bandini, Andrea; Valentino, Maria Euler characteristic and Akashi series for Selmer groups over global function fields. (English) Zbl 1410.11120 J. Number Theory 193, 213-234 (2018). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11R34 11R58 11G10 PDF BibTeX XML Cite \textit{A. Bandini} and \textit{M. Valentino}, J. Number Theory 193, 213--234 (2018; Zbl 1410.11120) Full Text: DOI arXiv
Rains, Eric M.; Sam, Steven V. Invariant theory of \(\bigwedge^3(9)\) and genus-2 curves. (English) Zbl 1405.15035 Algebra Number Theory 12, No. 4, 935-957 (2018). MSC: 15A72 14H60 14K05 PDF BibTeX XML Cite \textit{E. M. Rains} and \textit{S. V. Sam}, Algebra Number Theory 12, No. 4, 935--957 (2018; Zbl 1405.15035) Full Text: DOI
Matar, Ahmed Fine Selmer groups, Heegner points and anticyclotomic \(\mathbb{Z}_p\)-extensions. (English) Zbl 1441.11148 Int. J. Number Theory 14, No. 5, 1279-1304 (2018). Reviewer: Gabriel D. Villa Salvador (Ciudad de México) MSC: 11G05 11R23 PDF BibTeX XML Cite \textit{A. Matar}, Int. J. Number Theory 14, No. 5, 1279--1304 (2018; Zbl 1441.11148) Full Text: DOI arXiv
Hara, Takashi; Ochiai, Tadashi The cyclotomic Iwasawa main conjecture for Hilbert cusp forms with complex multiplication. (English) Zbl 1442.11145 Kyoto J. Math. 58, No. 1, 1-100 (2018). MSC: 11R23 11F41 11F67 PDF BibTeX XML Cite \textit{T. Hara} and \textit{T. Ochiai}, Kyoto J. Math. 58, No. 1, 1--100 (2018; Zbl 1442.11145) Full Text: DOI Euclid
Kidwell, Keenan On the structure of Selmer groups of \(p\)-ordinary modular forms over \(\mathbb{Z}_{p}\)-extensions. (English) Zbl 1403.11068 J. Number Theory 187, 296-331 (2018). Reviewer: Andrea Bandini (Parma) MSC: 11R23 PDF BibTeX XML Cite \textit{K. Kidwell}, J. Number Theory 187, 296--331 (2018; Zbl 1403.11068) Full Text: DOI
Lim, Meng Fai; Sujatha, Ramdorai Fine Selmer groups of congruent Galois representations. (English) Zbl 1430.11148 J. Number Theory 187, 66-91 (2018). MSC: 11R23 11R34 11F80 16S34 PDF BibTeX XML Cite \textit{M. F. Lim} and \textit{R. Sujatha}, J. Number Theory 187, 66--91 (2018; Zbl 1430.11148) Full Text: DOI arXiv
Elias, Yara; de Vera-Piquero, Carlos CM cycles on Kuga-Sato varieties over Shimura curves and Selmer groups. (English) Zbl 1445.11051 Forum Math. 30, No. 2, 321-346 (2018). MSC: 11G18 11G40 11R34 11F80 PDF BibTeX XML Cite \textit{Y. Elias} and \textit{C. de Vera-Piquero}, Forum Math. 30, No. 2, 321--346 (2018; Zbl 1445.11051) Full Text: DOI arXiv
Castella, Francesc; Hsieh, Ming-Lun Heegner cycles and \(p\)-adic \(L\)-functions. (English) Zbl 06837437 Math. Ann. 370, No. 1-2, 567-628 (2018). MSC: 11G40 11F80 11F67 11S40 PDF BibTeX XML Cite \textit{F. Castella} and \textit{M.-L. Hsieh}, Math. Ann. 370, No. 1--2, 567--628 (2018; Zbl 06837437) Full Text: DOI arXiv
Shankar, Arul; Wang, Xiaoheng Rational points on hyperelliptic curves having a marked non-Weierstrass point. (English) Zbl 1387.11035 Compos. Math. 154, No. 1, 188-222 (2018). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 14G05 14H25 PDF BibTeX XML Cite \textit{A. Shankar} and \textit{X. Wang}, Compos. Math. 154, No. 1, 188--222 (2018; Zbl 1387.11035) Full Text: DOI arXiv
Lim, Meng Fai Comparing the \(\pi\)-primary submodules of the dual Selmer groups. (English) Zbl 1434.11217 Asian J. Math. 21, No. 6, 1153-1182 (2017). MSC: 11R23 11R34 11F80 PDF BibTeX XML Cite \textit{M. F. Lim}, Asian J. Math. 21, No. 6, 1153--1182 (2017; Zbl 1434.11217) Full Text: DOI arXiv
Castella, Francesc; Kim, Chan-Ho; Longo, Matteo Variation of anticyclotomic Iwasawa invariants in Hida families. (English) Zbl 1404.11126 Algebra Number Theory 11, No. 10, 2339-2368 (2017). Reviewer: Andreas Nickel (Essen) MSC: 11R23 11F33 PDF BibTeX XML Cite \textit{F. Castella} et al., Algebra Number Theory 11, No. 10, 2339--2368 (2017; Zbl 1404.11126) Full Text: DOI arXiv
Jha, Somnath; Majumdar, Dipramit Functional equation for the Selmer group of nearly ordinary Hida deformation of Hilbert modular forms. (English) Zbl 1441.11275 Asian J. Math. 21, No. 3, 397-428 (2017). MSC: 11R23 11F41 11F33 11F80 PDF BibTeX XML Cite \textit{S. Jha} and \textit{D. Majumdar}, Asian J. Math. 21, No. 3, 397--428 (2017; Zbl 1441.11275) Full Text: DOI arXiv
Lim, Meng Fai Notes on the fine Selmer groups. (English) Zbl 1441.11277 Asian J. Math. 21, No. 2, 337-362 (2017). MSC: 11R23 11F80 11R34 11S25 16E65 PDF BibTeX XML Cite \textit{M. F. Lim}, Asian J. Math. 21, No. 2, 337--362 (2017; Zbl 1441.11277) Full Text: DOI arXiv
Chida, Masataka Selmer groups and central values of \(L\)-functions for modular forms. (Groupes de Selmer et valeurs centrales de fonctions \(L\) de formes modulaires.) (English. French summary) Zbl 1441.11119 Ann. Inst. Fourier 67, No. 3, 1231-1276 (2017). MSC: 11F67 11R23 PDF BibTeX XML Cite \textit{M. Chida}, Ann. Inst. Fourier 67, No. 3, 1231--1276 (2017; Zbl 1441.11119) Full Text: DOI
Kane, Daniel M.; Thorne, Jack A. On the \(\phi\)-Selmer groups of the elliptic curves \(y^2=x^3-Dx\). (English) Zbl 1432.11058 Math. Proc. Camb. Philos. Soc. 163, No. 1, 71-93 (2017). MSC: 11G05 14H52 PDF BibTeX XML Cite \textit{D. M. Kane} and \textit{J. A. Thorne}, Math. Proc. Camb. Philos. Soc. 163, No. 1, 71--93 (2017; Zbl 1432.11058) Full Text: DOI
Česnavičius, Kęstutis \(p\)-Selmer growth in extensions of degree \(p\). (English) Zbl 1396.11088 J. Lond. Math. Soc., II. Ser. 95, No. 3, 833-852 (2017). Reviewer: Mohammad Sadek (New Cairo) MSC: 11G10 11R34 11R58 PDF BibTeX XML Cite \textit{K. Česnavičius}, J. Lond. Math. Soc., II. Ser. 95, No. 3, 833--852 (2017; Zbl 1396.11088) Full Text: DOI
Castella, Francesc \(p\)-adic heights of Heegner points and Beilinson-Flach classes. (English) Zbl 1400.11138 J. Lond. Math. Soc., II. Ser. 96, No. 1, 156-180 (2017). Reviewer: Francesc Bars Cortina (Bellaterra) MSC: 11R23 11G05 11G40 PDF BibTeX XML Cite \textit{F. Castella}, J. Lond. Math. Soc., II. Ser. 96, No. 1, 156--180 (2017; Zbl 1400.11138) Full Text: DOI
Hatley, Jeffrey Rank parity for congruent supersingular elliptic curves. (English) Zbl 1374.14029 Proc. Am. Math. Soc. 145, No. 9, 3775-3786 (2017). Reviewer: Elisa Lorenzo García (Rennes) MSC: 14H52 11G05 11F80 11R23 PDF BibTeX XML Cite \textit{J. Hatley}, Proc. Am. Math. Soc. 145, No. 9, 3775--3786 (2017; Zbl 1374.14029) Full Text: DOI arXiv
Kim, Chan-Ho; Pollack, Robert; Weston, Tom On the freeness of anticyclotomic Selmer groups of modular forms. (English) Zbl 1428.11193 Int. J. Number Theory 13, No. 6, 1443-1455 (2017). MSC: 11R23 11F33 PDF BibTeX XML Cite \textit{C.-H. Kim} et al., Int. J. Number Theory 13, No. 6, 1443--1455 (2017; Zbl 1428.11193) Full Text: DOI
Büyükboduk, Kâzım; Lei, Antonio Integral Iwasawa theory of Galois representations for non-ordinary primes. (English) Zbl 1391.11150 Math. Z. 286, No. 1-2, 361-398 (2017). Reviewer: Andreas Nickel (Essen) MSC: 11R23 PDF BibTeX XML Cite \textit{K. Büyükboduk} and \textit{A. Lei}, Math. Z. 286, No. 1--2, 361--398 (2017; Zbl 1391.11150) Full Text: DOI
Ahmed, Suman; Aribam, Chandrakant; Shekhar, Sudhanshu Root numbers and parity of local Iwasawa invariants. (English) Zbl 1428.11105 J. Number Theory 177, 285-306 (2017). MSC: 11G05 11G07 11R23 14H52 PDF BibTeX XML Cite \textit{S. Ahmed} et al., J. Number Theory 177, 285--306 (2017; Zbl 1428.11105) Full Text: DOI
Chetty, Sunil Comparing local constants of ordinary elliptic curves in dihedral extensions. (English) Zbl 1407.11074 Funct. Approximatio, Comment. Math. 54, No. 2, 241-250 (2016). MSC: 11G05 11G07 11G40 PDF BibTeX XML Cite \textit{S. Chetty}, Funct. Approximatio, Comment. Math. 54, No. 2, 241--250 (2016; Zbl 1407.11074) Full Text: DOI Euclid
Le Hung, Bao V.; Li, Chao Level raising mod 2 and arbitrary 2-Selmer ranks. (English) Zbl 1423.11088 Compos. Math. 152, No. 8, 1576-1608 (2016). MSC: 11F33 11F80 11G05 11G10 PDF BibTeX XML Cite \textit{B. V. Le Hung} and \textit{C. Li}, Compos. Math. 152, No. 8, 1576--1608 (2016; Zbl 1423.11088) Full Text: DOI arXiv
Greenberg, Ralph On the structure of Selmer groups. (English) Zbl 1414.11140 Loeffler, David (ed.) et al., Elliptic curves, modular forms and Iwasawa theory. In honour of John H. Coates’ 70th birthday, Cambridge, UK, March 2015. Proceedings of the conference and the workshop. Cham: Springer. Springer Proc. Math. Stat. 188, 225-252 (2016). MSC: 11R23 11R34 PDF BibTeX XML Cite \textit{R. Greenberg}, Springer Proc. Math. Stat. 188, 225--252 (2016; Zbl 1414.11140) Full Text: DOI
Morrow, Jackson Salvatore Selmer groups of twists of elliptic curves over \(K\) with \(K\)-rational torsion points. (English) Zbl 1402.11087 Res. Number Theory 2, Paper No. 30, 23 p. (2016). MSC: 11G05 14G05 PDF BibTeX XML Cite \textit{J. S. Morrow}, Res. Number Theory 2, Paper No. 30, 23 p. (2016; Zbl 1402.11087) Full Text: DOI
Allen, Patrick B. Deformations of polarized automorphic Galois representations and adjoint Selmer groups. (English) Zbl 1417.11093 Duke Math. J. 165, No. 13, 2407-2460 (2016). MSC: 11F80 11F70 11R34 PDF BibTeX XML Cite \textit{P. B. Allen}, Duke Math. J. 165, No. 13, 2407--2460 (2016; Zbl 1417.11093) Full Text: DOI Euclid arXiv
Hida, Haruzo Arithmetic of adjoint \(L\)-values. (English) Zbl 1418.11084 Balasubramanyam, Baskar (ed.) et al., \(p\)-adic aspects of modular forms. Based on lectures at the ICTS program, IISER, Pune, India, June 10–20, 2014. Hackensack, NJ: World Scientific. 185-236 (2016). MSC: 11F60 20C08 PDF BibTeX XML Cite \textit{H. Hida}, in: \(p\)-adic aspects of modular forms. Based on lectures at the ICTS program, IISER, Pune, India, June 10--20, 2014. Hackensack, NJ: World Scientific. 185--236 (2016; Zbl 1418.11084) Full Text: DOI
Lai, King Fai; Longhi, Ignazio; Tan, Ki-Seng; Trihan, Fabien The Iwasawa main conjecture for constant ordinary abelian varieties over function fields. (English) Zbl 1347.11078 Proc. Lond. Math. Soc. (3) 112, No. 6, 1040-1058 (2016). Reviewer: Andrea Bandini (Parma) MSC: 11R23 11R34 11R58 11S40 11G10 PDF BibTeX XML Cite \textit{K. F. Lai} et al., Proc. Lond. Math. Soc. (3) 112, No. 6, 1040--1058 (2016; Zbl 1347.11078) Full Text: DOI arXiv
Skinner, Christopher Multiplicative reduction and the cyclotomic main conjecture for \(\mathrm{GL}_2\). (English) Zbl 1368.11060 Pac. J. Math. 283, No. 1, 171-200 (2016). Reviewer: Lawrence C. Washington (College Park) MSC: 11G40 11R23 11F67 PDF BibTeX XML Cite \textit{C. Skinner}, Pac. J. Math. 283, No. 1, 171--200 (2016; Zbl 1368.11060) Full Text: DOI arXiv
Shekhar, Sudhanshu Parity of ranks of elliptic curves with equivalent mod \(p\) Galois representations. (English) Zbl 1346.14086 Proc. Am. Math. Soc. 144, No. 8, 3255-3266 (2016). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 14H52 11F33 11R23 PDF BibTeX XML Cite \textit{S. Shekhar}, Proc. Am. Math. Soc. 144, No. 8, 3255--3266 (2016; Zbl 1346.14086) Full Text: DOI
Mazur, Barry; Rubin, Karl Controlling Selmer groups in the higher core rank case. (English. French summary) Zbl 1411.11065 J. Théor. Nombres Bordx. 28, No. 1, 145-183 (2016). MSC: 11G40 11R23 11R34 11F80 PDF BibTeX XML Cite \textit{B. Mazur} and \textit{K. Rubin}, J. Théor. Nombres Bordx. 28, No. 1, 145--183 (2016; Zbl 1411.11065) Full Text: DOI arXiv
Lundell, Benjamin Quantitative level lowering. (English) Zbl 1403.11045 Am. J. Math. 138, No. 2, 419-448 (2016). MSC: 11F80 11F41 PDF BibTeX XML Cite \textit{B. Lundell}, Am. J. Math. 138, No. 2, 419--448 (2016; Zbl 1403.11045) Full Text: DOI Link
Lim, Meng Fai Akashi series, characteristic elements and congruence of Galois representations. (English) Zbl 1341.11062 Int. J. Number Theory 12, No. 3, 593-613 (2016). Reviewer: Andrea Bandini (Parma) MSC: 11R23 11R34 11G05 11F80 PDF BibTeX XML Cite \textit{M. F. Lim}, Int. J. Number Theory 12, No. 3, 593--613 (2016; Zbl 1341.11062) Full Text: DOI arXiv
Valentino, Maria On Euler characteristics of Selmer groups for abelian varieties over global function fields. (English) Zbl 1341.11063 Arch. Math. 106, No. 2, 117-128 (2016). Reviewer: Andreas Nickel (Bielefeld) MSC: 11R23 11R34 PDF BibTeX XML Cite \textit{M. Valentino}, Arch. Math. 106, No. 2, 117--128 (2016; Zbl 1341.11063) Full Text: DOI arXiv
Yu, Myungjun Selmer ranks of twists of hyperelliptic curves and superelliptic curves. (English) Zbl 1334.11048 J. Number Theory 160, 148-185 (2016). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11G10 14K15 PDF BibTeX XML Cite \textit{M. Yu}, J. Number Theory 160, 148--185 (2016; Zbl 1334.11048) Full Text: DOI arXiv
Van Order, Jeanine On the dihedral Euler characteristics of Selmer groups of abelian varieties. (English) Zbl 1397.11096 Dieulefait, Luis (ed.) et al., Arithmetic and geometry. Proceedings of the research conference of the trimester, Bonn, Germany, April 15–19, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-46254-0/pbk; 978-1-316-10687-7/ebook). London Mathematical Society Lecture Note Series 420, 458-492 (2015). MSC: 11G05 11G10 11G40 11R23 PDF BibTeX XML Cite \textit{J. Van Order}, Lond. Math. Soc. Lect. Note Ser. 420, 458--492 (2015; Zbl 1397.11096) Full Text: arXiv
Benois, Denis Selmer complexes and \(p\)-adic Hodge theory. (English) Zbl 1388.11078 Dieulefait, Luis (ed.) et al., Arithmetic and geometry. Proceedings of the research conference of the trimester, Bonn, Germany, April 15–19, 2013. Cambridge: Cambridge University Press (ISBN 978-1-107-46254-0/pbk; 978-1-316-10687-7/ebook). London Mathematical Society Lecture Note Series 420, 36-88 (2015). MSC: 11S23 11R23 14C30 PDF BibTeX XML Cite \textit{D. Benois}, Lond. Math. Soc. Lect. Note Ser. 420, 36--88 (2015; Zbl 1388.11078)
Iovita, Adrian; Marmora, Adriano On the continuity of the finite Bloch-Kato cohomology. (English) Zbl 1387.11089 Rend. Semin. Mat. Univ. Padova 134, 239-271 (2015). MSC: 11S23 14F30 PDF BibTeX XML Cite \textit{A. Iovita} and \textit{A. Marmora}, Rend. Semin. Mat. Univ. Padova 134, 239--271 (2015; Zbl 1387.11089) Full Text: DOI
Elias, Yara Kolyvagin’s method for Chow groups of Kuga-Sato varieties over ring class fields. (English. French summary) Zbl 1398.11101 Ann. Math. Qué. 39, No. 2, 147-167 (2015). MSC: 11G40 11G18 14C15 PDF BibTeX XML Cite \textit{Y. Elias}, Ann. Math. Qué. 39, No. 2, 147--167 (2015; Zbl 1398.11101) Full Text: DOI arXiv
Lim, Meng Fai On the pseudo-nullity of the dual fine Selmer groups. (English) Zbl 1350.11099 Int. J. Number Theory 11, No. 7, 2055-2063 (2015). Reviewer: Cornelius Greither (Neubiberg) MSC: 11R23 11R34 PDF BibTeX XML Cite \textit{M. F. Lim}, Int. J. Number Theory 11, No. 7, 2055--2063 (2015; Zbl 1350.11099) Full Text: DOI arXiv
Wan, Xin The Iwasawa main conjecture for Hilbert modular forms. (English) Zbl 1379.11089 Forum Math. Sigma 3, Paper No. e18, 95 p. (2015). MSC: 11R23 11F41 PDF BibTeX XML Cite \textit{X. Wan}, Forum Math. Sigma 3, Paper No. e18, 95 p. (2015; Zbl 1379.11089) Full Text: DOI
Bhargava, Manjul; Kane, Daniel M.; Lenstra, Hendrik W. jun.; Poonen, Bjorn; Rains, Eric Modeling the distribution of ranks, Selmer groups, and Shafarevich-Tate groups of elliptic curves. (English) Zbl 1329.14071 Camb. J. Math. 3, No. 3, 275-321 (2015). Reviewer: Andrea Bandini (Parma) MSC: 14H52 11G05 14G15 PDF BibTeX XML Cite \textit{M. Bhargava} et al., Camb. J. Math. 3, No. 3, 275--321 (2015; Zbl 1329.14071) Full Text: DOI arXiv
Nekovář, Jan Compatibility of arithmetic and algebraic local constants (the case \(\ell \neq p\)). (English) Zbl 1335.11044 Compos. Math. 151, No. 9, 1626-1646 (2015). Reviewer: Andrea Bandini (Parma) MSC: 11G05 11G40 11S40 PDF BibTeX XML Cite \textit{J. Nekovář}, Compos. Math. 151, No. 9, 1626--1646 (2015; Zbl 1335.11044) Full Text: DOI
Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia Euler systems for modular forms over imaginary quadratic fields. (English) Zbl 1376.11050 Compos. Math. 151, No. 9, 1585-1625 (2015). MSC: 11F85 11F67 11G40 14G35 PDF BibTeX XML Cite \textit{A. Lei} et al., Compos. Math. 151, No. 9, 1585--1625 (2015; Zbl 1376.11050) Full Text: DOI arXiv
Ramachandran, Niranjan A note on the Bloch-Tamagawa space and Selmer groups. (English) Zbl 1378.11072 Proc. Japan Acad., Ser. A 91, No. 5, 61-65 (2015). MSC: 11G40 14K15 20G30 PDF BibTeX XML Cite \textit{N. Ramachandran}, Proc. Japan Acad., Ser. A 91, No. 5, 61--65 (2015; Zbl 1378.11072) Full Text: DOI arXiv
Ouyang, Yi; Zhang, Shenxing On second 2-descent and non-congruent numbers. (English) Zbl 1339.11067 Acta Arith. 170, No. 4, 343-360 (2015). Reviewer: Nikos Tzanakis (Iraklion) MSC: 11G05 11D25 PDF BibTeX XML Cite \textit{Y. Ouyang} and \textit{S. Zhang}, Acta Arith. 170, No. 4, 343--360 (2015; Zbl 1339.11067) Full Text: DOI
Bandini, Andrea; Bars, Francesc; Longhi, Ignazio Characteristic ideals and Selmer groups. (English) Zbl 1329.11116 J. Number Theory 157, 530-546 (2015). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11G35 PDF BibTeX XML Cite \textit{A. Bandini} et al., J. Number Theory 157, 530--546 (2015; Zbl 1329.11116) Full Text: DOI arXiv
Lamplugh, J. An analogue of the Washington-Sinnott theorem for elliptic curves with complex multiplication. I. (English) Zbl 1323.11035 J. Lond. Math. Soc., II. Ser. 91, No. 3, 609-642 (2015). Reviewer: Lawrence C. Washington (College Park) MSC: 11G05 11R23 11G40 11G15 11R29 PDF BibTeX XML Cite \textit{J. Lamplugh}, J. Lond. Math. Soc., II. Ser. 91, No. 3, 609--642 (2015; Zbl 1323.11035) Full Text: DOI
Lim, Meng Fai On completely faithful Selmer groups of elliptic curves and Hida deformations. (English) Zbl 1325.11054 J. Algebra 432, 72-90 (2015). Reviewer: Piotr Krasoń (Szczecin) MSC: 11F80 11G05 11R23 11R34 16S34 PDF BibTeX XML Cite \textit{M. F. Lim}, J. Algebra 432, 72--90 (2015; Zbl 1325.11054) Full Text: DOI arXiv
Lim, Meng Fai On the homology of Iwasawa cohomology groups. (English) Zbl 1400.11142 J. Ramanujan Math. Soc. 30, No. 1, 51-65 (2015). MSC: 11R23 11R34 11F80 PDF BibTeX XML Cite \textit{M. F. Lim}, J. Ramanujan Math. Soc. 30, No. 1, 51--65 (2015; Zbl 1400.11142) Full Text: arXiv
Česnavičius, Kęstutis Selmer groups and class groups. (English) Zbl 1319.11037 Compos. Math. 151, No. 3, 416-434 (2015). Reviewer: Davide Lombardo (Orsay) MSC: 11G10 11R23 11R29 11R58 PDF BibTeX XML Cite \textit{K. Česnavičius}, Compos. Math. 151, No. 3, 416--434 (2015; Zbl 1319.11037) Full Text: DOI arXiv
Bellaïche, Joël Unitary eigenvarieties at isobaric points. (English) Zbl 1396.11129 Can. J. Math. 67, No. 2, 315-329 (2015). MSC: 11S25 11F80 PDF BibTeX XML Cite \textit{J. Bellaïche}, Can. J. Math. 67, No. 2, 315--329 (2015; Zbl 1396.11129) Full Text: DOI
Mazur, Barry; Rubin, Karl Selmer companion curves. (English) Zbl 1316.11047 Trans. Am. Math. Soc. 367, No. 1, 401-421 (2015). Reviewer: Andrea Bandini (Parma) MSC: 11G05 11G40 11G07 PDF BibTeX XML Cite \textit{B. Mazur} and \textit{K. Rubin}, Trans. Am. Math. Soc. 367, No. 1, 401--421 (2015; Zbl 1316.11047) Full Text: DOI arXiv
Lim, Meng Fai A remark on the \(\mathfrak{M}_{H}(G)\)-conjecture and Akashi series. (English) Zbl 1319.11073 Int. J. Number Theory 11, No. 1, 269-297 (2015). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11R34 11G05 11F80 PDF BibTeX XML Cite \textit{M. F. Lim}, Int. J. Number Theory 11, No. 1, 269--297 (2015; Zbl 1319.11073) Full Text: DOI arXiv
Aribam, Chandrakant S. On the \(\mu\)-invariant of fine Selmer groups. (English) Zbl 1385.11067 J. Number Theory 135, 284-300 (2014). MSC: 11R23 11F33 11F80 11F85 PDF BibTeX XML Cite \textit{C. S. Aribam}, J. Number Theory 135, 284--300 (2014; Zbl 1385.11067) Full Text: DOI
Schaefer, Edward F. Corrigendum to: “Class groups and Selmer groups”. (English) Zbl 1384.11074 J. Number Theory 135, 390 (2014). MSC: 11G10 14K02 11R29 11R34 11G35 PDF BibTeX XML Cite \textit{E. F. Schaefer}, J. Number Theory 135, 390 (2014; Zbl 1384.11074) Full Text: DOI
Watkins, Mark; Donnelly, Stephen; Elkies, Noam D.; Fisher, Tom; Granville, Andrew; Rogers, Nicholas F. Ranks of quadratic twists of elliptic curves. (English) Zbl 1365.11070 Numéro consacré au trimestre “Méthodes arithmétiques et applications”, automne 2013. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2014, 2, 63-98 (2014). MSC: 11G05 11G40 14H52 PDF BibTeX XML Cite \textit{M. Watkins} et al., Publ. Math. Besançon, Algèbre Théor. Nombres 2014, 63--98 (2014; Zbl 1365.11070)
Pacheco, Amílcar On the rank of abelian varieties over a function field. (Sur le rang des variétés abéliennes sur un corps de fonctions.) (French. English summary) Zbl 1366.11082 Numéro consacré au trimestre “Méthodes arithmétiques et applications”, automne 2013. Besançon: Presses Universitaires de Franche-Comté. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2014, 2, 31-46 (2014). MSC: 11G10 PDF BibTeX XML Cite \textit{A. Pacheco}, Publ. Math. Besançon, Algèbre Théor. Nombres 2014, 31--46 (2014; Zbl 1366.11082)
Harron, Robert; Lei, Antonio Iwasawa theory for symmetric powers of CM modular forms at non-ordinary primes. (English) Zbl 1361.11066 J. Théor. Nombres Bordx. 26, No. 3, 673-707 (2014). MSC: 11R23 11F80 11F67 PDF BibTeX XML Cite \textit{R. Harron} and \textit{A. Lei}, J. Théor. Nombres Bordx. 26, No. 3, 673--707 (2014; Zbl 1361.11066) Full Text: DOI arXiv
Ohshita, Tatsuya Higher Fitting ideals of Iwasawa modules and Euler systems. (English) Zbl 1385.11069 RIMS Kôkyûroku Bessatsu B51, 139-149 (2014). MSC: 11R23 11R18 PDF BibTeX XML Cite \textit{T. Ohshita}, RIMS Kôkyûroku Bessatsu B51, 139--149 (2014; Zbl 1385.11069) Full Text: arXiv
Kurihara, Masato The structure of Selmer groups of elliptic curves and modular symbols. (English) Zbl 1361.11039 Bouganis, Thanasis (ed.) et al., Iwasawa theory 2012. State of the art and recent advances. Selected papers based on the presentations at the conference, Heidelberg, Germany, July 30 – August 3, 2012. Berlin: Springer (ISBN 978-3-642-55244-1/hbk; 978-3-642-55245-8/ebook). Contributions in Mathematical and Computational Sciences 7, 317-356 (2014). MSC: 11G05 11F67 11G50 PDF BibTeX XML Cite \textit{M. Kurihara}, Contrib. Math. Comput. Sci. 7, 317--356 (2014; Zbl 1361.11039) Full Text: DOI arXiv
Hsieh, Ming-Lun Iwasawa \(\mu\)-invariants of \(p\)-adic Hecke \(L\)-functions. (English) Zbl 1361.11067 Bouganis, Thanasis (ed.) et al., Iwasawa theory 2012. State of the art and recent advances. Selected papers based on the presentations at the conference, Heidelberg, Germany, July 30 – August 3, 2012. Berlin: Springer (ISBN 978-3-642-55244-1/hbk; 978-3-642-55245-8/ebook). Contributions in Mathematical and Computational Sciences 7, 247-263 (2014). MSC: 11R23 11M38 11-02 PDF BibTeX XML Cite \textit{M.-L. Hsieh}, Contrib. Math. Comput. Sci. 7, 247--263 (2014; Zbl 1361.11067) Full Text: DOI
Greenberg, Ralph On \(p\)-adic Artin \(L\)-functions. II. (English) Zbl 1356.11077 Bouganis, Thanasis (ed.) et al., Iwasawa theory 2012. State of the art and recent advances. Selected papers based on the presentations at the conference, Heidelberg, Germany, July 30 – August 3, 2012. Berlin: Springer (ISBN 978-3-642-55244-1/hbk; 978-3-642-55245-8/ebook). Contributions in Mathematical and Computational Sciences 7, 227-245 (2014). MSC: 11R23 11S25 11S40 11M38 PDF BibTeX XML Cite \textit{R. Greenberg}, Contrib. Math. Comput. Sci. 7, 227--245 (2014; Zbl 1356.11077) Full Text: DOI
Wan, Xin Introduction to Skinner-Urban’s work on the Iwasawa main conjecture for \(\mathrm{GL}_{2}\). (English) Zbl 1360.11115 Bouganis, Thanasis (ed.) et al., Iwasawa theory 2012. State of the art and recent advances. Selected papers based on the presentations at the conference, Heidelberg, Germany, July 30 – August 3, 2012. Berlin: Springer (ISBN 978-3-642-55244-1/hbk; 978-3-642-55245-8/ebook). Contributions in Mathematical and Computational Sciences 7, 35-61 (2014). MSC: 11R23 11F80 11F33 11F85 PDF BibTeX XML Cite \textit{X. Wan}, Contrib. Math. Comput. Sci. 7, 35--61 (2014; Zbl 1360.11115) Full Text: DOI
Longo, Matteo; Vigni, Stefano Vanishing of special values and central derivatives in Hida families. (English) Zbl 1359.11036 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 13, No. 3, 859-888 (2014). Reviewer: Xavier Guitart (MR3331531) MSC: 11F11 11G18 PDF BibTeX XML Cite \textit{M. Longo} and \textit{S. Vigni}, Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 13, No. 3, 859--888 (2014; Zbl 1359.11036) Full Text: DOI arXiv
Bandini, Andrea; Valentino, Maria On Selmer groups of abelian varieties over \(\ell\)-adic Lie extensions of global function fields. (English) Zbl 1316.11097 Bull. Braz. Math. Soc. (N.S.) 45, No. 3, 575-595 (2014). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 11R23 11G35 PDF BibTeX XML Cite \textit{A. Bandini} and \textit{M. Valentino}, Bull. Braz. Math. Soc. (N.S.) 45, No. 3, 575--595 (2014; Zbl 1316.11097) Full Text: DOI arXiv
Shekhar, Sudhanshu; Sujatha, R. Euler characteristic and congruences of elliptic curves. (English) Zbl 1318.11078 Münster J. Math. 7, No. 1, 327-343 (2014). Reviewer: Franz Lemmermeyer (Jagstzell) MSC: 11G05 14G25 14H52 PDF BibTeX XML Cite \textit{S. Shekhar} and \textit{R. Sujatha}, Münster J. Math. 7, No. 1, 327--343 (2014; Zbl 1318.11078)
Fisher, Tom; Newton, Rachel Computing the Cassels-Tate pairing on the 3-Selmer group of an elliptic curve. (English) Zbl 1314.11042 Int. J. Number Theory 10, No. 7, 1881-1907 (2014). Reviewer: Noburo Ishii (Kyoto) MSC: 11G05 11G07 16H05 PDF BibTeX XML Cite \textit{T. Fisher} and \textit{R. Newton}, Int. J. Number Theory 10, No. 7, 1881--1907 (2014; Zbl 1314.11042) Full Text: DOI arXiv
Lei, Antonio; Loeffler, David; Zerbes, Sarah Livia Euler systems for Rankin-Selberg convolutions of modular forms. (English) Zbl 1315.11044 Ann. Math. (2) 180, No. 2, 653-771 (2014). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11F80 11F85 11F67 14C15 PDF BibTeX XML Cite \textit{A. Lei} et al., Ann. Math. (2) 180, No. 2, 653--771 (2014; Zbl 1315.11044) Full Text: DOI arXiv
Bhargava, Manjul; Skinner, Christopher A positive proportion of elliptic curves over \(\mathbb Q\) have rank one. (English) Zbl 1315.11045 J. Ramanujan Math. Soc. 29, No. 2, 221-242 (2014). Reviewer: Andrea Bandini (Parma) MSC: 11G05 PDF BibTeX XML Cite \textit{M. Bhargava} and \textit{C. Skinner}, J. Ramanujan Math. Soc. 29, No. 2, 221--242 (2014; Zbl 1315.11045) Full Text: arXiv
Nomura, Jiro Annihilation of Selmer groups for monomial CM-extensions. (English) Zbl 1351.11036 J. Number Theory 144, 353-378 (2014). MSC: 11G10 11G40 PDF BibTeX XML Cite \textit{J. Nomura}, J. Number Theory 144, 353--378 (2014; Zbl 1351.11036) Full Text: DOI
Sano, Takamichi A generalization of Darmon’s conjecture for Euler systems for general \(p\)-adic representations. (English) Zbl 1296.11143 J. Number Theory 144, 281-324 (2014). MSC: 11R29 11R27 11R37 11F85 PDF BibTeX XML Cite \textit{T. Sano}, J. Number Theory 144, 281--324 (2014; Zbl 1296.11143) Full Text: DOI arXiv
Trihan, Fabien; Yasuda, Seidai The \(\ell\)-parity conjecture for abelian varieties over function fields of characteristic \(p>0\). (English) Zbl 1301.11056 Compos. Math. 150, No. 4, 507-522 (2014). Reviewer: Francesc Bars Cortina (Bellaterra) MSC: 11G40 11G20 PDF BibTeX XML Cite \textit{F. Trihan} and \textit{S. Yasuda}, Compos. Math. 150, No. 4, 507--522 (2014; Zbl 1301.11056) Full Text: DOI