Nonabelian Galois cohomology

Abstract

This § is devoted to the illustration of a “general principle”, which can be stated roughly as follows:

Let K/k be a field extension, and let X be an “object” denned over k. We shall say that an object Y, defined over k, is a K/k-form of X if Y becomes isomorphic to X when the ground field is extended to K. The classes of such forms (for the equivalence relation defined by the k-isomorphisms) form a set E(K/k, X).