Hoshi, Yuichiro; Mochizuki, Shinichi Topics surrounding the combinatorial anabelian geometry of hyperbolic curves. IV: Discreteness and sections. (English) Zbl 07960606 Nagoya Math. J. 256, 785-885 (2024). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: DOI
Betts, L. Alexander The motivic anabelian geometry of local heights on abelian varieties. (English) Zbl 07946548 Memoirs of the American Mathematical Society 1518. Providence, RI: American Mathematical Society (AMS) (ISBN 978-1-4704-7124-8/pbk; 978-1-4704-7969-5/ebook). v, 88 p. (2024). Reviewer: Andrzej Dąbrowski (Szczecin) MSC: 11-02 11G50 11G10 11G25 14G40 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Iijima, Yu On a geometric version of the Grothendieck conjecture for configuration spaces of hyperbolic curves. (English) Zbl 07940341 Hokkaido Math. J. 53, No. 3, 531-548 (2024). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Creutz, Brendan; Voloch, Jose Felipe Etale descent obstruction and anabelian geometry of curves over finite fields. (English) Zbl 07885170 Épijournal de Géom. Algébr., EPIGA 8, Paper No. 10, 10 p. (2024). Reviewer: Christophe Ritzenthaler (Nice) MSC: 11G20 11G30 14G05 14G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tsujimura, Shota Birational anabelian Grothendieck conjecture for curves over arbitrary cyclotomic extension fields of number fields. (English) Zbl 1548.14090 Adv. Math. 435, Part B, Article ID 109380, 41 p. (2023). MSC: 14H05 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Porowski, Wojciech Pro-\(p\) criterion of good reduction of punctured elliptic curves. (English) Zbl 1541.14047 Publ. Res. Inst. Math. Sci. 59, No. 4, 843-882 (2023). MSC: 14H30 11G07 × Cite Format Result Cite Review PDF Full Text: DOI
Tsujimura, Shota On the semi-absoluteness of isomorphisms between the pro-\(p\) arithmetic fundamental groups of smooth varieties. (English) Zbl 1534.14030 Publ. Res. Inst. Math. Sci. 59, No. 3, 507-541 (2023). MSC: 14H30 14H25 × Cite Format Result Cite Review PDF Full Text: DOI
Tsujimura, Shota On the tempered fundamental groups of hyperbolic curves of genus \(0\) over \(\overline{\mathbb{Q}}_p\). (English) Zbl 1534.14029 J. Inst. Math. Jussieu 22, No. 6, 2833-2856 (2023). MSC: 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Yu On topological and combinatorial structures of pointed stable curves over algebraically closed fields of positive characteristic. (English) Zbl 1531.14036 Math. Nachr. 296, No. 8, 3740-3781 (2023). Reviewer: Rodolfo Aguilar Aguilar (Sofia) MSC: 14G32 14H30 14F35 × Cite Format Result Cite Review PDF Full Text: DOI
Shimizu, Ryoji Isomorphisms of Galois groups of number fields with restricted ramification. (English) Zbl 1541.11099 Math. Nachr. 296, No. 7, 3026-3033 (2023); correction ibid. 297, No. 5, 1978 (2024). Reviewer: George Janelidze (Cape Town) MSC: 11R32 11S15 11R45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gaulhiac, Sylvain Towards tempered anabelian behaviour of Berkovich annuli. (Vers un comportement anabélien tempéré des couronnes de Berkovich.) (English. French summary) Zbl 1530.14053 Bull. Soc. Math. Fr. 151, No. 1, 1-36 (2023). MSC: 14H30 12J25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Murotani, Takahiro A study on anabelian geometry of higher local fields. (English) Zbl 1524.11213 Int. J. Number Theory 19, No. 6, 1229-1248 (2023). MSC: 11S20 14G20 14H30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Yamaguchi, Naganori The geometrically \(m\)-step solvable Grothendieck conjecture for genus 0 curves over finitely generated fields. (English) Zbl 1527.14072 J. Algebra 629, 191-226 (2023). MSC: 14H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gaulhiac, Sylvain Anabelian reconstruction of the skeleton of analytic curves. (Reconstruction anabélienne du squelette des courbes analytiques.) (French. English summary) Zbl 07688673 Ann. Inst. Fourier 73, No. 3, 999-1084 (2023). MSC: 14H30 12J25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hoshi, Yuichiro The geometry of hyperbolic curvoids. (English) Zbl 1518.14044 Publ. Res. Inst. Math. Sci. 59, No. 1, 1-55 (2023). MSC: 14H30 14G32 × Cite Format Result Cite Review PDF Full Text: DOI
Hoshi, Yuichiro Mono-anabelian reconstruction of solvably closed Galois extensions of number fields. (English) Zbl 1531.11106 J. Math. Sci., Tokyo 29, No. 3, 257-283 (2022). Reviewer: Bouchaïb Sodaïgui (Valenciennes) MSC: 11R32 × Cite Format Result Cite Review PDF Full Text: Link
Hoshi, Yuichiro; Minamide, Arata; Mochizuki, Shinichi Group-theoreticity of numerical invariants and distinguished subgroups of configuration space groups. (English) Zbl 1511.14050 Kodai Math. J. 45, No. 3, 295-348 (2022). MSC: 14H30 14G32 14H10 × Cite Format Result Cite Review PDF Full Text: DOI
Minamide, Arata; Tsujimura, Shota Internal indecomposability of profinite groups. (English) Zbl 07605934 Adv. Math. 409, Part B, Article ID 108689, 17 p. (2022). Reviewer: Egle Bettio (Venezia) MSC: 20E18 12E30 × Cite Format Result Cite Review PDF Full Text: DOI
Porowski, Wojciech Anabelian reconstruction of the Néron-Tate local height function. (English) Zbl 1497.14051 Eur. J. Math. 8, No. 3, 1172-1195 (2022). MSC: 14H30 14H25 × Cite Format Result Cite Review PDF Full Text: DOI
Higashiyama, Kazumi The semi-absolute anabelian geometry of geometrically pro-\(p\) arithmetic fundamental groups of associated low-dimensional configuration spaces. (English) Zbl 1507.14043 Publ. Res. Inst. Math. Sci. 58, No. 3, 579-634 (2022). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Hoshi, Yuichiro; Nishio, Yu On the outer automorphism groups of the absolute Galois groups of mixed-characteristic local fields. (English) Zbl 1511.11094 Res. Number Theory 8, No. 3, Paper No. 56, 13 p. (2022). Reviewer: Günter Lettl (Graz) MSC: 11S20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Sarashina, Akira Conditional reconstruction of affine open subschemes of elliptic curves in positive characteristic by their geometric fundamental groups. (English) Zbl 1512.11056 Int. J. Number Theory 18, No. 7, 1465-1490 (2022). MSC: 11G07 11G20 14H30 14H52 14G32 11G05 20E18 × Cite Format Result Cite Review PDF Full Text: DOI
Minamide, Arata; Tsujimura, Shota Anabelian group-theoretic properties of the absolute Galois groups of discrete valuation fields. (English) Zbl 1493.12009 J. Number Theory 239, 298-334 (2022). MSC: 12F10 12J25 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Hoshi, Yuichiro; Mochizuki, Shinichi Topics surrounding the combinatorial anabelian geometry of hyperbolic curves II. Tripods and combinatorial cuspidalization. (English) Zbl 1520.11002 Lecture Notes in Mathematics 2299. Singapore: Springer (ISBN 978-981-19-1095-1/pbk; 978-981-19-1096-8/ebook). xxiii, 150 p. (2022). Reviewer: Jeroen Sijsling (Ulm) MSC: 11-02 14-02 11Gxx 14H30 14G40 × Cite Format Result Cite Review PDF Full Text: DOI
Takao, Naotake Anabelian geometry of certain types of hyperbolic polycurves. (English) Zbl 1498.14079 J. Algebra 604, 406-428 (2022). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: DOI
Yang, Yu Maximum generalized Hasse-Witt invariants and their applications to anabelian geometry. (English) Zbl 1520.14061 Sel. Math., New Ser. 28, No. 1, Paper No. 5, 98 p. (2022). MSC: 14H30 14G17 14G32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hoshi, Yuichiro Introduction to mono-anabelian geometry. (English. French summary) Zbl 1506.14055 Algèbre et théorie des nombres 2021. Publications Mathématiques de Besançon. Algèbre et Théorie des Nombres 2021. Besançon: Presses Universitaires de Franche-Comté. 5-44 (2021). MSC: 14G45 11S20 × Cite Format Result Cite Review PDF Full Text: Link
Cadoret, Anna; Pirutka, Alena Reconstructing function fields from Milnor \(K\)-theory. (English) Zbl 1492.19002 Algebra Number Theory 15, No. 9, 2261-2288 (2021). Reviewer: Bernhard Köck (Southampton) MSC: 19D45 12F99 11R70 11R58 14C35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tsujimura, Shota Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks. (English) Zbl 1489.14040 Kodai Math. J. 44, No. 3, 492-555 (2021). MSC: 14H30 14H10 14A20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Fesenko, Ivan Class field theory, its three main generalisations, and applications. (English) Zbl 1482.11152 EMS Surv. Math. Sci. 8, No. 1-2, 107-133 (2021). Reviewer: Abdelmalek Azizi (Oujda) MSC: 11R37 11S37 12-03 19F05 × Cite Format Result Cite Review PDF Full Text: DOI
Litt, Daniel Arithmetic representations of fundamental groups. II: Finiteness. (English) Zbl 1520.14041 Duke Math. J. 170, No. 8, 1851-1897 (2021). MSC: 14F35 11G99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Backlinks: MO
Hoshi, Yuichiro; Murotani, Takahiro; Tsujimura, Shota On the geometric subgroups of the étale fundamental groups of varieties over real closed fields. (English) Zbl 1462.14027 Math. Z. 298, No. 1-2, 215-229 (2021). MSC: 14G27 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Mochizuki, Shinichi Inter-universal Teichmüller theory. I: Construction of Hodge theaters. (English) Zbl 1465.14002 Publ. Res. Inst. Math. Sci. 57, No. 1-2, 3-207 (2021). Reviewer: Peter Scholze (Bonn) MSC: 14-02 14H25 14H30 14G32 × Cite Format Result Cite Review PDF Full Text: DOI Backlinks: MO MO
Bresciani, Giulio Some implications between Grothendieck’s anabelian conjectures. (English) Zbl 1468.14046 Algebr. Geom. 8, No. 2, 231-267 (2021). MSC: 14F35 14F30 11G35 14A20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hoshi, Yuichiro Reconstruction of profinite graphs from profinite groups of PIPSC-type. (English) Zbl 1457.14069 Hokkaido Math. J. 49, No. 3, 399-430 (2020). MSC: 14H30 20E18 14G32 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Tsujimura, Shota Geometric version of the Grothendieck conjecture for universal curves over Hurwitz stacks: a research announcement. (English) Zbl 1455.14062 RIMS Kôkyûroku Bessatsu B83, 217-233 (2020). MSC: 14H30 14H10 14A20 × Cite Format Result Cite Review PDF Full Text: Link
Higashiyama, Kazumi Reconstruction of function fields from pro-\(p\) second configuration space groups, a research announcement. (Japanese. English summary) Zbl 1455.14059 RIMS Kôkyûroku Bessatsu B83, 205-215 (2020). MSC: 14H30 14G32 14H10 × Cite Format Result Cite Review PDF Full Text: Link
Minamide, Arata On a direct product decomposition related to the Grothendieck-Teichmüller group. (Japanese. English summary) Zbl 1455.14060 RIMS Kôkyûroku Bessatsu B83, 195-203 (2020). MSC: 14H30 14G32 14H10 × Cite Format Result Cite Review PDF Full Text: Link
Yang, Yu The anabelian geometry of curves over algebraically closed fields of positive characteristic: a survey. (English) Zbl 1455.14051 RIMS Kôkyûroku Bessatsu B83, 47-58 (2020). MSC: 14G32 14H30 × Cite Format Result Cite Review PDF Full Text: Link
Takao, Naotake Recent progress in higher-dimensional anabelian geometry. (English) Zbl 1454.14085 RIMS Kôkyûroku Bessatsu B77, 203-213 (2020). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: Link
Sawada, Koichiro Pro-\(p\) and cohomological aspects of anabelian geometry of hyperbolic polycurves. (English) Zbl 1454.14084 RIMS Kôkyûroku Bessatsu B77, 191-202 (2020). MSC: 14H30 14H10 14H25 20J06 × Cite Format Result Cite Review PDF Full Text: Link
Tsujimura, Shota Combinatorial Belyi cuspidalization and arithmetic subquotients of the Grothendieck-Teichmüller group. (English) Zbl 1460.14068 Publ. Res. Inst. Math. Sci. 56, No. 4, 779-829 (2020). MSC: 14H30 × Cite Format Result Cite Review PDF Full Text: DOI Link
Hoshi, Yuichiro Topics in the anabelian geometry of mixed-characteristic local fields. (English) Zbl 1505.11145 Hiroshima Math. J. 49, No. 3, 323-398 (2019). MSC: 11S20 14H30 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Takahashi, Nobuyoshi Quandles associated to Galois covers of arithmetic schemes. (English) Zbl 1435.14024 Kyushu J. Math. 73, No. 1, 145-164 (2019). Reviewer: Michel Waldschmidt (Paris) MSC: 14G32 20N02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bogomolov, Fedor A.; Rovinsky, Marat; Tschinkel, Yuri Homomorphisms of multiplicative groups of fields preserving algebraic dependence. (English) Zbl 1431.14018 Eur. J. Math. 5, No. 3, 656-685 (2019). Reviewer: Thong Nguyen Quang Do (Besançon) MSC: 14G32 11R32 11R58 14E08 19D45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Yang, Yu Group-theoretic characterizations of almost open immersions of curves. (English) Zbl 1504.14059 J. Algebra 530, 290-325 (2019). MSC: 14H30 11G20 14G32 × Cite Format Result Cite Review PDF Full Text: DOI
Murotani, Takahiro A \(p\)-adic analytic approach to the absolute Grothendieck conjecture. (English) Zbl 1440.14156 Publ. Res. Inst. Math. Sci. 55, No. 2, 401-451 (2019). MSC: 14H30 11S20 14G05 14G20 × Cite Format Result Cite Review PDF Full Text: DOI Link
Higashiyama, Kazumi Reconstruction of inertia groups associated to log divisors from a configuration space group equipped with its collection of log-full subgroups. (English) Zbl 1411.14029 Math. J. Okayama Univ. 61, 37-73 (2019). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF
Cornelissen, Gunther; Li, Xin; Marcolli, Matilde; Smit, Harry Reconstructing global fields from dynamics in the abelianized Galois group. (English) Zbl 1431.11110 Sel. Math., New Ser. 25, No. 2, Paper No. 24, 18 p. (2019). Reviewer: Thomas Schmidt (Corvallis) MSC: 11M55 11R37 11R42 11R56 14H30 46N55 58B34 82C10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Lüdtke, Martin A birational anabelian reconstruction theorem for curves over algebraically closed fields in arbitrary characteristic. (English) Zbl 1417.11108 Isr. J. Math. 227, No. 2, 987-1011 (2018). Reviewer: Ivo M. Michailov (Shumen) MSC: 11G05 14G32 14H05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Nagamachi, Ippei On a good reduction criterion for proper polycurves with sections. (English) Zbl 1451.11056 Hiroshima Math. J. 48, No. 2, 223-251 (2018). MSC: 11G20 11G30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Euclid
Yang, Yu On the admissible fundamental groups of curves over algebraically closed fields of characteristic \(p>0\). (English) Zbl 1439.14102 Publ. Res. Inst. Math. Sci. 54, No. 3, 649-678 (2018). MSC: 14H30 14G32 × Cite Format Result Cite Review PDF Full Text: DOI
Sawada, Koichiro Cohomology of the geometric fundamental group of hyperbolic polycurves. (English) Zbl 1428.20051 J. Algebra 508, 364-389 (2018). MSC: 20J06 14H30 20E18 × Cite Format Result Cite Review PDF Full Text: DOI
Ivanov, Alexander B. On a generalization of the Neukirch-Uchida theorem. (English) Zbl 1432.11165 Mosc. Math. J. 17, No. 3, 371-383 (2017). MSC: 11R34 11R37 14G32 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Hoshi, Yuichiro; Kinoshita, Ryo; Nakayama, Chikara The Grothendieck conjecture for the moduli spaces of hyperbolic curves of genus one. (English) Zbl 1402.14034 Kodai Math. J. 40, No. 3, 625-637 (2017). MSC: 14H10 14G32 20F34 14H30 × Cite Format Result Cite Review PDF Full Text: DOI Euclid Link
Bogomolov, Fedor; Tschinkel, Yuri Universal spaces for unramified Galois cohomology. (English) Zbl 1437.12002 Auel, Asher (ed.) et al., Brauer groups and obstruction problems. Moduli spaces and arithmetic. Basel: Birkhäuser/Springer. Prog. Math. 320, 57-86 (2017). MSC: 12G05 11R58 14H05 20J06 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pop, Florian The \(\mathbb{Z}/p\) metabelian birational \(p\)-adic section conjecture for varieties. (English) Zbl 1428.11120 Compos. Math. 153, No. 7, 1433-1445 (2017). MSC: 11G20 14G05 14G32 × Cite Format Result Cite Review PDF Full Text: DOI
Saïdi, Mohamed; Tamagawa, Akio A refined version of Grothendieck’s birational anabelian conjecture for curves over finite fields. (English) Zbl 1388.14090 Adv. Math. 310, 610-662 (2017). Reviewer: Jeroen Sijsling (Ulm) MSC: 14H30 11G20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Schmidt, Alexander; Stix, Jakob Anabelian geometry with étale homotopy types. (English) Zbl 1405.14053 Ann. Math. (2) 184, No. 3, 817-868 (2016). Reviewer: Feng-Wen An (Hubei) MSC: 14F42 14H30 14G32 14F35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Patrikis, Stefan; Voloch, José; Zarhin, Yuri Anabelian geometry and descent obstructions on moduli spaces. (English) Zbl 1410.11086 Algebra Number Theory 10, No. 6, 1191-1219 (2016). MSC: 11G35 14G05 14G35 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kucharczyk, Robert A. On copies of the absolute Galois group in \(\operatorname{Out}F_{2}\). (English) Zbl 1383.11081 Proc. Am. Math. Soc. 144, No. 6, 2351-2359 (2016). MSC: 11G05 11G32 11R32 14G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Pop, Florian On the minimized decomposition theory of valuations. (English) Zbl 1363.12002 Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér. 58(106), No. 3, 331-357 (2015). MSC: 12E30 12F10 12G99 × Cite Format Result Cite Review PDF
Mochizuki, Shinichi Topics in absolute anabelian geometry. III: Global reconstruction algorithms. (English) Zbl 1358.14024 J. Math. Sci., Tokyo 22, No. 4, 939-1156 (2015). Reviewer: Gerd Faltings (Bonn) MSC: 14H30 14G32 14H25 11G32 × Cite Format Result Cite Review PDF Full Text: Link
Borne, Niels; Emsalem, Michel; Stix, Jakob Lifting Galois sections along torsors. (English) Zbl 1405.14074 Math. Nachr. 288, No. 17-18, 1939-1951 (2015). MSC: 14H30 14G05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fesenko, Ivan Arithmetic deformation theory via arithmetic fundamental groups and non-Archimedean theta-functions, notes on the work of Shinichi Mochizuki. (English) Zbl 1416.11119 Eur. J. Math. 1, No. 3, 405-440 (2015). MSC: 11G99 14G05 11G05 14D22 14G40 × Cite Format Result Cite Review PDF Full Text: DOI
Mochizuki, Shinichi Monomorphisms in categories of log schemes. (English) Zbl 1401.14011 Kodai Math. J. 38, No. 2, 365-429 (2015). MSC: 14A15 14G40 × Cite Format Result Cite Review PDF Full Text: DOI Euclid Link
Mochizuki, Shinichi A panoramic overview of inter-universal Teichmüller theory. (English) Zbl 1403.14061 RIMS Kôkyûroku Bessatsu B51, 301-345 (2014). MSC: 14H25 14H30 × Cite Format Result Cite Review PDF
Borne, Niels; Emsalem, Michel A criterion of cuspidalization of \(\ell\)-adic sections. (Un critère d’épointage des sections \(\ell\)-adiques.) (French. English summary) Zbl 1327.14103 Bull. Soc. Math. Fr. 142, No. 3, 465-487 (2014). MSC: 14F30 14G32 14H30 14F20 14G05 × Cite Format Result Cite Review PDF Full Text: arXiv Link
Ivanov, A. On some anabelian properties of arithmetic curves. (English) Zbl 1329.11120 Manuscr. Math. 144, No. 3-4, 545-564 (2014). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 11R34 11R37 14G32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Saïdi, Mohamed A local-global principle for torsors under geometric prosolvable fundamental groups. (English) Zbl 1297.11066 Manuscr. Math. 145, No. 1-2, 163-174 (2014). Reviewer: Lars Kindler (Berlin) MSC: 11G30 14H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mochizuki, Shinichi Topics in absolute anabelian geometry. II: Decomposition groups and endomorphisms. (English) Zbl 1367.14011 J. Math. Sci., Tokyo 20, No. 2, 171-269 (2013). MSC: 14H30 14H25 × Cite Format Result Cite Review PDF
Lepage, Emmanuel Resolution of nonsingularities for Mumford curves. (English) Zbl 1304.14026 Publ. Res. Inst. Math. Sci. 49, No. 4, 861-891 (2013). Reviewer: Jérôme Poineau (Caen) MSC: 14G22 14H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Stix, Jakob Birational \(p\)-adic Galois sections in higher dimensions. (English) Zbl 1306.14007 Isr. J. Math. 198, 49-61 (2013). Reviewer: Hiroaki Nakamura (Osaka) MSC: 14G32 12J20 14H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Saïdi, Mohamed On the \(p\)-adic section conjecture. (English) Zbl 1262.14029 J. Pure Appl. Algebra 217, No. 3, 583-584 (2013). Reviewer: Lars Kindler (Berlin) MSC: 14H30 14G20 × Cite Format Result Cite Review PDF Full Text: DOI
Hoshi, Yuichiro; Mochizuki, Shinichi Topics surrounding the combinatorial anabelian geometry of hyperbolic curves I: Inertia groups and profinite Dehn twists. (English) Zbl 1321.14018 Nakamura, Hiroaki (ed.) et al., Galois-Teichmüller theory and arithmetic geometry. Selected papers based on the presentations at the workshop and conference, Kyoto, Japan, October 25–30, 2010. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-014-3/hbk). Advanced Studies in Pure Mathematics 63, 659-811 (2012). MSC: 14G32 14H30 × Cite Format Result Cite Review PDF
Stix, Jakob On cuspidal sections of algebraic fundamental groups. (English) Zbl 1321.14027 Nakamura, Hiroaki (ed.) et al., Galois-Teichmüller theory and arithmetic geometry. Selected papers based on the presentations at the workshop and conference, Kyoto, Japan, October 25–30, 2010. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-014-3/hbk). Advanced Studies in Pure Mathematics 63, 519-563 (2012). MSC: 14H30 14G32 14G05 12E30 14F35 × Cite Format Result Cite Review PDF Full Text: arXiv
Schmidt, Alexander Motivic aspects of anabelian geometry. (English) Zbl 1321.14020 Nakamura, Hiroaki (ed.) et al., Galois-Teichmüller theory and arithmetic geometry. Selected papers based on the presentations at the workshop and conference, Kyoto, Japan, October 25–30, 2010. Tokyo: Mathematical Society of Japan (ISBN 978-4-86497-014-3/hbk). Advanced Studies in Pure Mathematics 63, 503-517 (2012). MSC: 14G32 14F42 18F20 × Cite Format Result Cite Review PDF
Harari, David; Stix, Jakob Descent obstruction and fundamental exact sequence. (English) Zbl 1315.14032 Stix, Jakob (ed.), The arithmetic of fundamental groups. PIA 2010. Based on a meeting, Heidelberg, Germany, February 8–12, 2010. Berlin: Springer (ISBN 978-3-642-23904-5/hbk; 978-3-642-23905-2/ebook). Contributions in Mathematical and Computational Sciences 2, 147-166 (2012). MSC: 14G05 14G32 14H30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mochizuki, Shinichi Topics in absolute anabelian geometry I: Generalities. (English) Zbl 1267.14039 J. Math. Sci., Tokyo 19, No. 2, 139-242 (2012). Reviewer: Tamás Szamuely (Budapest) MSC: 14H30 14H25 × Cite Format Result Cite Review PDF Full Text: Link
Pop, Florian Recovering function fields from their decomposition graphs. (English) Zbl 1309.12004 Goldfeld, Dorian (ed.) et al., Number theory, analysis and geometry. In memory of Serge Lang. Berlin: Springer (ISBN 978-1-4614-1259-5/hbk; 978-1-4614-1260-1/ebook). 519-594 (2012). MSC: 12E30 12F10 14G32 14H05 × Cite Format Result Cite Review PDF Full Text: DOI
Saïdi, Mohamed Around the Grothendieck anabelian section conjecture. (English) Zbl 1261.14012 Coates, John (ed.) et al., Non-abelian fundamental groups and Iwasawa theory. Cambridge: Cambridge University Press (ISBN 978-1-107-64885-2/pbk). London Mathematical Society Lecture Note Series 393, 72-106 (2012). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14G32 12F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Pop, Florian Lectures on anabelian phenomena in geometry and arithmetic. (English) Zbl 1303.11123 Coates, John (ed.) et al., Non-abelian fundamental groups and Iwasawa theory. Cambridge: Cambridge University Press (ISBN 978-1-107-64885-2/pbk). London Mathematical Society Lecture Note Series 393, 1-55 (2012). MSC: 11R23 11R32 11R29 14G32 × Cite Format Result Cite Review PDF Full Text: DOI
Hoshi, Yuichiro; Mochizuki, Shinichi On the combinatorial anabelian geometry of nodally nondegenerate outer representations. (English) Zbl 1264.14041 Hiroshima Math. J. 41, No. 3, 275-342 (2011). MSC: 14H30 14H10 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Saïdi, Mohamed; Tamagawa, Akio On the Hom-form of Grothendieck’s birational anabelian conjecture in positive characteristic. (English) Zbl 1235.14026 Algebra Number Theory 5, No. 2, 131-184 (2011). Reviewer: Tamás Szamuely (Budapest) MSC: 14H30 11G20 14G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Hoshi, Yuichiro Existence of nongeometric pro-\(p\) Galois sections of hyperbolic curves. (English) Zbl 1222.14057 Publ. Res. Inst. Math. Sci. 46, No. 4, 829-848 (2010). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14H30 11G30 14H25 × Cite Format Result Cite Review PDF
Pop, Florian On the birational \(p\)-adic section conjecture. (English) Zbl 1210.11072 Compos. Math. 146, No. 3, 621-637 (2010). Reviewer: Florin Nicolae (Berlin) MSC: 11G20 14G05 12E30 14G20 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Bogomolov, Fedor; Korotiaev, Mikhail; Tschinkel, Yuri A Torelli theorem for curves over finite fields. (English) Zbl 1193.14036 Pure Appl. Math. Q. 6, No. 1, 245-294 (2010). Reviewer: Jonathan Pila (Oxford) MSC: 14H25 14C34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Stix, Jakob On the period-index problem in light of the section conjecture. (English) Zbl 1198.14025 Am. J. Math. 132, No. 1, 157-180 (2010). Reviewer: Gunther Cornelissen (Utrecht) MSC: 14H30 11G30 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Stix, Jakob Trading degree for dimension in the section conjecture: the non-abelian Shapiro lemma. (English) Zbl 1190.14028 Math. J. Okayama Univ. 52, 29-43 (2010). Reviewer: Jérôme Poineau (Strasbourg) MSC: 14H30 14G05 20E22 × Cite Format Result Cite Review PDF Full Text: arXiv
Saïdi, Mohamed; Tamagawa, Akio On the anabelian geometry of hyperbolic curves over finite fields. (English) Zbl 1206.11081 RIMS Kôkyûroku Bessatsu B12, 67-89 (2009). Reviewer: Scott Corry (Appleton) MSC: 11G20 14G15 14H30 14H25 × Cite Format Result Cite Review PDF
Hoshi, Yuichiro Absolute anabelian cuspidalizations of configuration spaces of proper hyperbolic curves over finite fields. (English) Zbl 1202.14027 Publ. Res. Inst. Math. Sci. 45, No. 3, 661-744 (2009). Reviewer: Andrew Obus (New York) MSC: 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Harari, David; Szamuely, Tamás Galois sections for abelianized fundamental groups. (English) Zbl 1180.14027 Math. Ann. 344, No. 4, 779-800 (2009). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14H30 11G10 11R32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Mochizuki, Shinichi The étale theta function and its Frobenioid-theoretic manifestations. (English) Zbl 1170.14023 Publ. Res. Inst. Math. Sci. 45, No. 1, 227-349 (2009). Reviewer: Fumio Hazama (Hatoyama) MSC: 14H42 14H30 × Cite Format Result Cite Review PDF Full Text: DOI
Corry, Scott; Pop, Florian The pro-\(p\) hom-form of the birational anabelian conjecture. (English) Zbl 1168.14016 J. Reine Angew. Math. 628, 121-127 (2009). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14G20 12F10 14H25 14H30 12F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Hoshi, Yuichiro On the fundamental groups of log configuration schemes. (English) Zbl 1169.14022 Math. J. Okayama Univ. 51, 1-26 (2009). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14H30 14H10 × Cite Format Result Cite Review PDF
Pop, Florian Galois theory of Zariski prime divisors. (English) Zbl 1177.12005 Bertrand, Daniel (ed.) et al., Groupes de Galois arithmétique et différentiels. Paris: Société Mathématique de France (ISBN 978-2-85629-222-8/pbk). Séminaires et Congrès 13, 293-312 (2006). Reviewer: Manouchehr Misaghian (Prairie View) MSC: 12E30 12J10 12F10 × Cite Format Result Cite Review PDF
Saïdi, Mohamed On complete families of curves with a given fundamental group in positive characteristic. (English) Zbl 1129.14044 Manuscr. Math. 118, No. 4, 425-441 (2005). Reviewer: Hiroaki Nakamura (Okayama) MSC: 14H30 14F20 14G32 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Szamuely, Tamás Galois groups of fields of finite type (following Pop). (Groupes de Galois de corps de type fini (d’après Pop).) (French) Zbl 1148.12300 Séminaire Bourbaki. Volume 2002/2003. Exposés 909–923. Paris: Société Mathématique de France (ISBN 2-85629-156-2/pbk). Astérisque 294, 403-431, Exp. No. 923 (2004). MSC: 12F10 14E15 14H25 14J20 × Cite Format Result Cite Review PDF
Mochizuki, Shinichi Categorical representation of locally Noetherian log schemes. (English) Zbl 1073.14002 Adv. Math. 188, No. 1, 222-246 (2004). Reviewer: Andreas Cap (Wien) MSC: 14A15 14A20 18F99 × Cite Format Result Cite Review PDF Full Text: DOI Backlinks: MO
Stix, Jakob Projective anabelian curves in positive characteristic and descent theory for log-étale covers. (English) Zbl 1077.14040 Bonner Mathematische Schriften 354. Bonn: Univ. Bonn, Mathematisches Institut (Diss.). xi, 118 p. (2002). Reviewer: Werner Kleinert (Berlin) MSC: 14H30 14E20 14H10 14G15 11G25 × Cite Format Result Cite Review PDF