# Galois cohomology

In the mathematical branch of number theory, Galois **cohomology** is the study of the group cohomology of Galois groups .

Is *L* | *K* is a field extension and *A* a *Galoismodul* , so a module of the Galois group Gal ( *L* | *K* ), we write

- (for notation see the article group cohomology )

If especially *L* = *K *^{sep is} a separable closure of *K* , then one also writes

One of the first results of Galois cohomology is Hilbert's Theorem 90 , which says:

- .

Especially in class field theory , the relationship between Galois cohomology and brewer group is important:

- .

## literature

- Jean Pierre Serre: Galois cohomology . Springer, Berlin 2002, ISBN 3-540-42192-0 .