Galois cohomology

Under Galoiskohomologie is understood in the mathematical branch of number theory, the study of Gruppenkohomologie of Galois groups.

If L | K is a field extension and A is a Galois, ie a module under the Galois group Gal ( L | K), one writes

If, in particular L = KSEP a separable degree of K, then we write also

One of the first results of the Galoiskohomologie is Hilbert's theorem 90, which states:

Especially in the class field theory, the relationship between Galoiskohomologie and Brauer group is important: