Rapinchuk, Andrei; Rapinchuk, Igor The finiteness of the Tate-Shafarevich group over function fields for algebraic tori defined over the base field. (La finitude du groupe de Tate-Shafarevich sur les corps de fonctions pour les tores algébriques définis sur le corps de base.) (English. French summary) Zbl 07915248 C. R., Math., Acad. Sci. Paris 362, 739-749 (2024). MSC: 14Lxx 14Exx 14Gxx × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Abramenko, Peter; Rapinchuk, Andrei S.; Rapinchuk, Igor A. Applications of the fixed point theorem for group actions on buildings to algebraic groups over polynomial rings. (English) Zbl 07877985 J. Algebra 656, 3-23 (2024). Reviewer: Cameron Ruether (Ottawa) MSC: 20G15 20G07 20E45 14L15 20E42 20E07 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gille, Stefan; Panin, Ivan On the Gersten conjecture for Hermitian Witt groups. (English) Zbl 07850197 Math. Ann. 389, No. 2, 1187-1224 (2024). Reviewer: Adam Chapman (Tel Hai) MSC: 11E70 11E81 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chernousov, Vladimir I.; Rapinchuk, Andrei S.; Rapinchuk, Igor A. Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction. (English) Zbl 1547.11052 Adv. Math. 438, Article ID 109437, 78 p. (2024). Reviewer: Yong Hu (Guangdong) MSC: 11E72 14L15 20G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gille, Philippe; Moret-Bailly, Laurent Principal bundles and adeles. (Fibrés principaux et adèles.) (French. English summary) Zbl 07851389 Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 24, No. 4, 2403-2429 (2023). MSC: 20G35 11R56 14L30 11D88 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
First, Uriya A. An 8-periodic exact sequence of Witt groups of Azumaya algebras with involution. (English) Zbl 1521.11021 Manuscr. Math. 170, No. 1-2, 313-407 (2023). Reviewer: Adam Chapman (Tel Hai) MSC: 11E81 16H05 19G12 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Colliot-Thélène, Jean-Louis; Harbater, David; Hartmann, Julia; Krashen, Daniel; Parimala, R.; Suresh, V. Local-global principles for constant reductive groups over semi-global fields. (English) Zbl 1502.14059 Mich. Math. J. 72, 77-144 (2022). Reviewer: B. Z. Moroz (Bonn) MSC: 14G12 14D10 14G20 14F20 14L15 11G20 05C05 20G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Link
Harari, David; Szamuely, Tamás On Tate-Shafarevich groups of one-dimensional families of commutative group schemes over number fields. (English) Zbl 1527.14051 Math. Z. 302, No. 2, 935-948 (2022). Reviewer: Nithi Rungtanapirom (Bangkok) MSC: 14G05 14G25 14F22 11E72 11R34 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Guo, N. The Grothendieck-Serre conjecture over semilocal Dedekind rings. (English) Zbl 1506.14096 Transform. Groups 27, No. 3, 897-917 (2022). Reviewer: Uriya A. First (Vancouver) MSC: 14L15 20G10 14F20 20G25 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Laga, Jef The average size of the 2-Selmer group of a family of non-hyperelliptic curves of genus 3. (English) Zbl 1518.11052 Algebra Number Theory 16, No. 5, 1161-1212 (2022). Reviewer: Dimitros Poulakis (Thessaloniki) MSC: 11G30 11E72 11N45 14G05 14G25 14H40 14H45 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fedorov, Roman On the Grothendieck-Serre conjecture about principal bundles and its generalizations. (English) Zbl 1485.14089 Algebra Number Theory 16, No. 2, 447-465 (2022). MSC: 14L15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Česnavičius, Kęstutis Grothendieck-Serre in the quasi-split unramified case. (English) Zbl 1492.14081 Forum Math. Pi 10, Paper No. e9, 30 p. (2022). Reviewer: Uriya A. First (Vancouver) MSC: 14L15 11E81 14M17 20G10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Česnavičius, Kęstutis Problems about torsors over regular rings. (English) Zbl 1495.14074 Acta Math. Vietnam. 47, No. 1, 39-107 (2022). Reviewer: Moshe Roitman (Haifa) MSC: 14M17 14L15 20G10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fedorov, Roman On the Grothendieck-Serre conjecture on principal bundles in mixed characteristic. (English) Zbl 1490.14079 Trans. Am. Math. Soc. 375, No. 1, 559-586 (2022). Reviewer: Jiuzu Hong (New Haven) MSC: 14L15 14D10 14M17 20G35 20G41 11E08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rapinchuk, Andrei S.; Rapinchuk, Igor A. Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields. (English) Zbl 1489.11059 J. Number Theory 233, 228-260 (2022). MSC: 11E72 14F20 14L15 11R34 14G40 20G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gille, P.; Parimala, R.; Suresh, V. Local triviality for \(G\)-torsors. (English) Zbl 1478.14028 Math. Ann. 380, No. 1-2, 539-567 (2021). MSC: 14D23 14F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Panin, I. Notes on a Grothendieck-Serre conjecture in mixed characteristic case. (English) Zbl 1454.14115 J. Math. Sci., New York 252, No. 6, 841-848 (2021) and Zap. Nauchn. Semin. POMI 484, 138-148 (2019). MSC: 14L15 14G45 20G05 20G35 × Cite Format Result Cite Review PDF Full Text: DOI
Panin, Ivan A. Two purity theorems and the Grothendieck-Serre conjecture concerning principal \(\mathbf{G}\)-bundles. (English. Russian original) Zbl 1460.14099 Sb. Math. 211, No. 12, 1777-1794 (2020); translation from Mat. Sb. 211, No. 12, 123-142 (2020). MSC: 14L15 20G35 20G40 20G10 14J60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Rapinchuk, Andrei S.; Rapinchuk, Igor A. Linear algebraic groups with good reduction. (English) Zbl 1466.20032 Res. Math. Sci. 7, No. 3, Paper No. 28, 65 p. (2020). MSC: 20G05 11E72 14G05 14L15 20E15 20-02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Panin, I. A short exact sequence. (English) Zbl 1451.14136 J. Math. Sci., New York 251, No. 3, 419-426 (2020) and Zap. Nauchn. Semin. POMI 485, 176-186 (2019). MSC: 14L15 20G99 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bayer-Fluckiger, E.; First, U. A.; Huruguen, M. Orders that are étale-locally isomorphic. (English) Zbl 1458.16019 St. Petersbg. Math. J. 31, No. 4, 573-584 (2020) and Algebra Anal. 31, No. 4, 1-15 (2019). Reviewer: Adam Chapman (Tel Hai) MSC: 16H10 16W10 11E57 11E72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Tsybyshev, A. A step towards the mixed-characteristic Grothendieck-Serre conjecture. (English. Russian original) Zbl 1442.14145 St. Petersbg. Math. J. 31, No. 1, 181-187 (2020); translation from Algebra Anal. 31, No. 1, 246-254 (2019). MSC: 14L15 14F20 × Cite Format Result Cite Review PDF Full Text: DOI
Colliot-Thélène, J.-L.; Harbater, D.; Hartmann, J.; Krashen, D.; Parimala, R.; Suresh, V. Local-global principles for zero-cycles on homogeneous spaces over arithmetic function fields. (English) Zbl 1440.14035 Trans. Am. Math. Soc. 372, No. 8, 5263-5286 (2019). Reviewer: Yongqi Liang (Hefei) MSC: 14C25 14G05 14H25 11E72 12G05 12F10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bhaskhar, Nivedita; Chernousov, Vladimir; Merkurjev, Alexander The norm principle for type \(D_n\) groups over complete discretely valued fields. (English) Zbl 1515.20265 Trans. Am. Math. Soc. 372, No. 1, 97-117 (2019). MSC: 20G15 11E72 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asok, Aravind; Hoyois, Marc; Wendt, Matthias Generically split octonion algebras and \(\mathbb{A}^1\)-homotopy theory. (English) Zbl 1430.14051 Algebra Number Theory 13, No. 3, 695-747 (2019). Reviewer: Pavel Sechin (Heidelberg) MSC: 14F42 14L30 20G41 57T20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv Backlinks: MO
Zhu, Yi Homogeneous space fibrations over surfaces. (English) Zbl 1440.14052 J. Inst. Math. Jussieu 18, No. 2, 293-327 (2019). MSC: 14D06 14M17 14M22 14D23 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Asok, Aravind; Hoyois, Marc; Wendt, Matthias Affine representability results in \(\mathbb A^1\)-homotopy theory. II: Principal bundles and homogeneous spaces. (English) Zbl 1400.14061 Geom. Topol. 22, No. 2, 1181-1225 (2018). Reviewer: Fangzhou Jin (Essen) MSC: 14F42 55R15 14L10 20G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bayer-Fluckiger, Eva; First, Uriya A. Patching and weak approximation in isometry groups. (English) Zbl 1427.11036 Trans. Am. Math. Soc. 369, No. 11, 7999-8035 (2017). MSC: 11E39 11E41 16H10 14L17 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Panin, I. A.; Stavrova, A. K. On the Grothendieck-Serre conjecture concerning principal \(G\)-bundles over semilocal Dedekind domains. (English. Russian original) Zbl 1362.14048 J. Math. Sci., New York 222, No. 4, 453-462 (2017); translation from Zap. Nauchn. Semin. POMI 443, 133-146 (2016). MSC: 14L15 20G35 13F05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Bayer-Fluckiger, Eva; First, Uriya A. Rationally isomorphic Hermitian forms and torsors of some non-reductive groups. (English) Zbl 1383.11045 Adv. Math. 312, 150-184 (2017). Reviewer: Andrew Dolphin (Antwerpen) (MR3635808) MSC: 11E39 14F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Chernousov, Vladimir; Gille, Philippe; Pianzola, Arturo A classification of torsors over Laurent polynomial rings. (English) Zbl 1362.14022 Comment. Math. Helv. 92, No. 1, 37-55 (2017). Reviewer: Vyacheslav A. Artamonov (Moskva) MSC: 14F20 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Bhaskhar, Nivedita On Serre’s injectivity question and norm principle. (English) Zbl 1342.14098 Comment. Math. Helv. 91, No. 1, 145-161 (2016). Reviewer: Wen-Wei Li (Beijing) MSC: 14L35 20G10 20G15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fedorov, Roman; Panin, Ivan A proof of the Grothendieck-Serre conjecture on principal bundles over regular local rings containing infinite fields. (English) Zbl 1330.14077 Publ. Math., Inst. Hautes Étud. Sci. 122, 169-193 (2015). Reviewer: Xiao Xiao (Utica) MSC: 14L15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Thǎńg, Nguyêñ Quôć A norm principle for class groups of reductive group schemes over Dedekind rings of integers of local and global fields. (English) Zbl 1370.11052 Vietnam J. Math. 43, No. 2, 257-281 (2015). Reviewer: Sebastian Petersen (Kassel) MSC: 11E72 14F20 14L15 14G20 14G25 18G50 20G10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Gille, Philippe; Pianzola, Arturo Torsors, reductive group schemes and extended affine Lie algebras. (English) Zbl 1354.17017 Mem. Am. Math. Soc. 1063, v, 112 p. (2013). MSC: 17B67 11E72 14F35 14L15 14L30 18G50 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Douai, Jean-Claude 2-cohomology of semi-simple simply connected group-schemes over curves defined over \(p\)-adic fields. (English. French summary) Zbl 1282.14045 J. Théor. Nombres Bordx. 25, No. 2, 307-316 (2013). Reviewer: Xiao Xiao (Utica) MSC: 14G20 14L05 14F22 11G20 × Cite Format Result Cite Review PDF Full Text: DOI
Chernousov, Vladimir; Merkurjev, Alexander Essential \(p\)-dimension of split simple groups of type \(A_n\). (English) Zbl 1284.11066 Math. Ann. 357, No. 1, 1-10 (2013). Reviewer: Emre Coskun (Ankara) MSC: 11E72 16K50 20G15 14L30 × Cite Format Result Cite Review PDF Full Text: DOI
Frenkel, Edward Langlands program, trace formulas, and their geometrization. (English) Zbl 1329.11121 Bull. Am. Math. Soc., New Ser. 50, No. 1, 1-55 (2013). MSC: 11R39 14D24 22E57 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Banaszak, Grzegorz; Gajda, Wojciech; Krasoń, Piotr On the image of Galois \(l\)-adic representations for abelian varieties of type III. (English) Zbl 1202.14042 Tohoku Math. J. (2) 62, No. 2, 163-189 (2010). Reviewer: Alan Koch (Decatur) MSC: 14K15 17B45 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyêñ Quôć Thăńg Corestriction principle for non-abelian cohomology of reductive group schemes over arithmetical rings. (English) Zbl 1143.11014 Proc. Japan Acad., Ser. A 82, No. 9, 147-151 (2006). Reviewer: Boris Kunyavskii (Ramat Gan) MSC: 11E72 14F20 14G20 14G25 14L15 18G50 20G10 20G25 20G30 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Pianzola, A. Affine Kac-Moody Lie algebras as torsors over the punctured line. (English) Zbl 1029.17021 Indag. Math., New Ser. 13, No. 2, 249-257 (2002). Reviewer: Dražen Adamović (Zagreb) MSC: 17B67 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Alev, Jacques; Ooms, Alfons; Van den Bergh, Michel A class of counterexamples to the Gel’fand-Kirillov conjecture. (English) Zbl 0853.17006 Trans. Am. Math. Soc. 348, No. 5, 1709-1716 (1996). Reviewer: Yu.N.Mal’tsev (Barnaul) MSC: 17B35 16K40 × Cite Format Result Cite Review PDF Full Text: DOI
Nguyêñ Quôć Thăńg Some local-global principles in the arithmetic of algebraic groups over real function fields. (English) Zbl 0842.20038 Math. Z. 221, No. 1, 1-19 (1996). Reviewer: Nguŷeñ Quôć Thăńg (Hamilton) MSC: 20G15 11E57 × Cite Format Result Cite Review PDF Full Text: DOI
Douai, Jean-Claude Homogeneous spaces and arithmetic of reductive group schemes over Dedekind rings. (Espaces homogènes et arithmétique des schémas en groupes réductifs sur les anneaux de Dedekind.) (French) Zbl 0862.14033 J. Théor. Nombres Bordx. 7, No. 1, 21-26 (1995). MSC: 14M17 18G50 14L30 55R40 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML EMIS
Colliot-Thélène, J.-L.; Sansuc, J.-J. Principal homogeneous spaces under flasque tori; applications. (English) Zbl 0597.14014 J. Algebra 106, No. 1, 148-205 (1987). MSC: 14F20 14M17 13B02 14L30 20G10 × Cite Format Result Cite Review PDF Full Text: DOI