From: jriou@clipper.ens.fr (Joel Riou)
Subject: Re: Galois cohomology
Date: 2 Feb 2001 18:24:51 GMT
Newsgroups: sci.math
Summary: Hilbert's Theorem 90 (cohomology groups are trivial)

Nick Halloway , dans le message (sci.math:390500), a écrit :
> I heard that the first cohomology group for the action of a finite Galois
> group on the additive or multiplicative subgroups of a field is = 1. 

Let K/k be a finite Galois extension, and G the Galois group. Then the
fact that H^1(G;K^*)=0 is known as the Hilbert 90 theorem.
For the additive group, for all i>=1, H^i(G;K)=0. 

A reference for Galois cohomology is Local fields, Jean-Pierre Serre.

-- 
Joël Riou - Joel.Riou@ens.fr