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 .