A norm principle for class groups of reductive group schemes over Dedekind rings of integers of local and global fields

DOI10.1007/s10013-015-0122-6zbMath1370.11052OpenAlexW2170378173MaRDI QIDQ2351172

Nguyêñ Quôć Thǎńg

Publication date: 23 June 2015

Published in: Vietnam Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: http://hdl.handle.net/21.11116/0000-0004-1448-5

zbMATH Keywords

norm principlereductive group schemesnon-abelian cohomologycorestriction map

Mathematics Subject Classification ID

Nonabelian homological algebra (category-theoretic aspects) (18G50) Étale and other Grothendieck topologies and (co)homologies (14F20) Local ground fields in algebraic geometry (14G20) Cohomology theory for linear algebraic groups (20G10) Global ground fields in algebraic geometry (14G25) Galois cohomology of linear algebraic groups (11E72) Group schemes (14L15)

Related Items (4)

On analogs of Cassels-Tate's exact sequence for connected reductive groups and Brauer-Manin obstruction for homogeneous spaces over global function fields ⋮ On Galois cohomology of connected reductive groups and Kottwitz exact sequence ⋮ A building-theoretic approach to relative Tamagawa numbers of semisimple groups over global function fields ⋮ On the genera of semisimple groups defined over an integral domain of a global function field

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Weil and Grothendieck approaches to adelic points
• Abelian class groups of reductive group schemes
• Equivalent conditions for (weak) corestriction principle for non-abelian étale cohomology of group schemes
• Nombres de Tamagawa et groupes unipotents en caractéristique p
• Finiteness theorems for discrete subgroups of bounded covolume in semi- simple groups
• Addendum to: Finiteness theorems for discrete subgroups of bounded covolume in semi-simple groups
• Stable trace formula: Elliptic singular terms
• Principal homogeneous spaces under flasque tori; applications
• Locally trivial principal homogeneous spaces
• Arithmetisch definierte Gruppen mit Galoisoperation
• Galois cohomology in degree three and homogeneous varieties
• The \(R\)-equivalence on reductive algebraic groups defined over a global field
• Weak corestriction principle for non-Abelian Galois cohomology
• On corestriction principle in non-abelian Galois cohomology over local and global fields.
• Weak approximation, Brauer and \(R\)-equivalence in algebraic groups over arithmetical fields. II.
• On Galois cohomology of semisimple groups over local and global fields of positive characteristic. III
• Corestriction principle for non-abelian cohomology of reductive group schemes over arithmetical rings
• On Galois cohomology of semisimple groups over local and global fields of positive characteristic
• Some finiteness properties of adele groups over number fields
• Halbeinfache Gruppenschemata über Dedekindringen
• Schémas en groupes. II: Groupes de type multiplicatif, et structure des schémas en groupes généraux. Exposés VIII à XVIII. Séminaire de Géométrie Algébrique du Bois Marie 1962/64 (SGA 3) dirigé par Michel Demazure et Alexander Grothendieck. Revised reprint
• Le défaut d'approximation forte dans les groupes linéaires connexes
• Finiteness theorems for algebraic groups over function fields
• Starke Approximation in algebraischen Gruppen. I.

This page was built for publication: A norm principle for class groups of reductive group schemes over Dedekind rings of integers of local and global fields