scholarly journals On Galois cohomology and weak approximation of connected reductive groups over fields of positive characteristic

2011 ◽  
Vol 87 (10) ◽  
pp. 203-208 ◽  
Author(s):  
Nguyen Quoc Thang
Keyword(s):  
Positive Characteristic ◽  
Galois Cohomology ◽  
Weak Approximation ◽  
Reductive Groups

The Distributions in the Invariant Trace Formula Are Supported on Characters

2000 ◽  
Vol 52 (4) ◽  
pp. 804-814 ◽  
Author(s):  
Robert E. Kottwitz ◽  
Jonathan D. Rogawski
Keyword(s):  
Trace Formula ◽  
Galois Cohomology ◽  
Invariant Form ◽  
Reductive Groups ◽  
Connected Case

AbstractJ. Arthur put the trace formula in invariant form for all connected reductive groups and certain disconnected ones. However his work was written so as to apply to the general disconnected case, modulo two missing ingredients. This paper supplies one of those missing ingredients, namely an argument in Galois cohomology of a kind first used by D. Kazhdan in the connected case.

scholarly journals Galois cohomology of real quasi-connected reductive groups

2022 ◽  
Author(s):  
Mikhail Borovoi ◽  
Andrei A. Gornitskii ◽  
Zev Rosengarten
Keyword(s):  
Galois Cohomology ◽  
Reductive Groups

Abelian Galois cohomology of reductive groups

1998 ◽  
Vol 132 (626) ◽  
pp. 0-0 ◽  
Author(s):  
Mikhail Borovoi
Keyword(s):  
Galois Cohomology ◽  
Reductive Groups

scholarly journals UN SCINDAGE DU MORPHISME DE FROBENIUS SUR L’ALGÈBRE DES DISTRIBUTIONS D’UN GROUPE RÉDUCTIF

2019 ◽  
Vol 71 (1) ◽  
pp. 197-206
Author(s):  
Michel Gros ◽  
Kaneda Masaharu
Keyword(s):  
Nous Avons ◽  
Algebraic Group ◽  
Positive Characteristic ◽  
Closed Field ◽  
Reductive Groups ◽  
Algebraically Closed Field ◽  
Frobenius Endomorphism ◽  
Simply Connected ◽  
Simplement Connexe ◽  
Field Of Positive Characteristic

Abstract Pour un groupe algébrique semi-simple simplement connexe sur un corps algébriquement clos de caractéristique positive, nous avons précédemment construit un scindage de l’endomorphisme de Frobenius sur son algèbre des distributions. Nous généralisons la construction au cas de des groupes réductifs connexes et en dégageons les corollaires correspondants. For a simply connected semisimple algebraic group over an algebraically closed field of positive characteristic we have already constructed a splitting of the Frobenius endomorphism on its algebra of distributions. We generalize the construction to the case of general connected reductive groups and derive the corresponding corollaries.

scholarly journals Infinitesimal Invariants in a Function Algebra

2009 ◽  
Vol 61 (4) ◽  
pp. 950-960 ◽  
Author(s):  
Rudolf Tange
Keyword(s):  
Simple Group ◽  
Mild Condition ◽  
Positive Characteristic ◽  
Function Algebra ◽  
Linear Algebraic Group ◽  
Closed Field ◽  
Reductive Groups ◽  
Regular Functions ◽  
Simply Connected ◽  
Field Of Positive Characteristic

Abstract.Let G be a reductive connected linear algebraic group over an algebraically closed field of positive characteristic and let 𝔤 be its Lie algebra. First we extend a well-known result about the Picard group of a semi-simple group to reductive groups. Then we prove that if the derived group is simply connected and 𝔤 satisfies a mild condition, the algebra K[G]𝔤 of regular functions on G that are invariant under the action of 𝔤 derived from the conjugation action is a unique factorisation domain.

Sign in / Sign up

Export Citation Format

Share Document