Galois cohomology

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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: