Continuous Non-abelian H¹ with Profinite Coefficients

Abstract

We recall the theory of non-abelian first cohomology as presented in Serre (Galois Cohomology, 1997) I §5 and emphasize the role played by conjugacy classes of sections and by equivariant torsors. The difference between two sections can be described by either a cocycle or an equivariant torsor.The analogue in the non-abelian setup of the familiar abelian long exact sequences for short exact sequences of coefficients or of low degree terms in the Hochschild–Serre spectral sequence turn out to exist but in a restricted form depending on the amount of commutativity that one is willing to spend as an assumption.