Some finiteness results for algebraic groups and unramified cohomology over higher-dimensional fields

DOI10.1016/j.jnt.2021.07.001zbMath1489.11059arXiv2002.01520OpenAlexW3183394764WikidataQ114156834 ScholiaQ114156834MaRDI QIDQ2064331

Igor A. Rapinchuk, Andrei S. Rapinchuk

Publication date: 5 January 2022

Published in: Journal of Number Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/2002.01520

zbMATH Keywords

Galois cohomologyunramified cohomologyalgebraic toriarithmetic of algebraic groups

Mathematics Subject Classification ID

Linear algebraic groups over arbitrary fields (20G15) Étale and other Grothendieck topologies and (co)homologies (14F20) Arithmetic varieties and schemes; Arakelov theory; heights (14G40) Galois cohomology of linear algebraic groups (11E72) Galois cohomology (11R34) Group schemes (14L15)

Related Items (4)

On some finiteness properties of algebraic groups over finitely generated fields ⋮ On Tate-Shafarevich groups of one-dimensional families of commutative group schemes over number fields ⋮ Hasse principles for quadratic forms over function fields ⋮ Simple algebraic groups with the same maximal tori, weakly commensurable Zariski-dense subgroups, and good reduction

Cites Work

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• On some finiteness properties of algebraic groups over finitely generated fields
• Degree three unramified cohomology of Severi-Brauer varieties
• Fibres quadratiques et composantes connexes réelles
• Generic splitting fields of central simple algebras
• Smallness of fundamental groups for arithmetic schemes
• Additive reduction of algebraic tori
• Cohomologie étale. Seminaire de géométrie algébrique du Bois-Marie SGA 4 1/2 par P. Deligne, avec la collaboration de J. F. Boutot, A. Grothendieck, L. Illusie et J. L. Verdier
• Applications of weight-two motivic cohomology
• Maximality of hyperspecial compact subgroups avoiding Bruhat-Tits theory
• Some finiteness results for the group \(SK_1\) of a biquaternion algebra
• The finiteness of the genus of a finite-dimensional division algebra, and some generalizations
• Linear algebraic groups with good reduction
• Isotriviality and étale cohomology of Laurent polynomial rings
• Schémas en groupes. III: Structure des schémas en groupes réductifs. Exposés XIX à XXVI. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3), dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• On the size of the genus of a division algebra
• Spinor groups with good reduction
• Sur le groupe des classes d’un schéma arithmétique
• A Hasse principle for two dimensional global fields.
• A.D. Alexandrov spaces with curvature bounded below
• The multipliers of similitudes and the Brauer group of homogeneous varieties.
• Pseudo-reductive Groups
• Galois Groups and Fundamental Groups
• Division algebras with the same maximal subfields
• Finiteness theorems for algebraic groups over function fields

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