# Galois cohomology of reductive groups over number fields

Seminar
Speaker
Mikhail Borovoi (Tel Aviv University)
Date
24/05/2023 - 11:30 - 10:30Add to Calendar 2023-05-24 10:30:00 2023-05-24 11:30:00 Galois cohomology of reductive groups over number fields Let G be a connected reductive group over a global field F (a number field or a global function field). Let M=\pi_1(G) denote the *algebraic fundamental group* of G, which is a certain finitely generated abelian group endowed with an action of the absolute Galois group Gal(F^s/F). Using and generalizing a result of Tate for tori, we give a closed formula for the Galois cohomology set  H^1(F,G)  in terms of the Galois module M and the Galois cohomology sets H^1(F_v,G) for the *real* places v of F.   Moreover, let T be an F-torus and let M=\pi_1(T)=X_*(T) denote the cocharacter group of T. We give a closed formula for H^2(F,T) in terms of the Galois module M.   This is a joint work with Tasho Kaletha: https://arxiv.org/abs/2303.04120 ================================================ https://us02web.zoom.us/j/87856132062 Meeting ID: 878 5613 2062   Third floor seminar room and Zoom אוניברסיטת בר-אילן - Department of Mathematics mathoffice@math.biu.ac.il Asia/Jerusalem public
Place
Third floor seminar room and Zoom
Abstract

Let G be a connected reductive group over a global field F (a number field or a global function field). Let M=\pi_1(G) denote the *algebraic fundamental group* of G, which is a certain finitely generated abelian group endowed with an action of the absolute Galois group Gal(F^s/F). Using and generalizing a result of Tate for tori, we give a closed formula for the Galois cohomology set  H^1(F,G)  in terms of the Galois module M and the Galois cohomology sets H^1(F_v,G) for the *real* places v of F.

Moreover, let T be an F-torus and let M=\pi_1(T)=X_*(T) denote the cocharacter group of T. We give a closed formula for H^2(F,T) in terms of the Galois module M.

This is a joint work with Tasho Kaletha: https://arxiv.org/abs/2303.04120

================================================

https://us02web.zoom.us/j/87856132062

Meeting ID: 878 5613 2062

Last Updated Date : 21/04/2023