Galois cohomology is the group cohomology of a Galois group acting on a module. For a discrete -module , the first group is the quotient of crossed homomorphisms by maps .
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Galois cohomology is a branch of mathematics that studies objects known as "cohomology groups" in the context of Galois theory, which is a part of algebra concerned with the symmetries of polynomial equations. To understand Galois cohomology, we start with a few key ideas: 1. **Galois Groups**: A Galois group is a group associated with a field extension, representing the symmetries of the roots of polynomials.