Non-abelian hypercohomology of a group with coefficients in a crossed module, and Galois cohomology

Abstract

We develop a hypercohomology theory of a group with coefficients in a crossed module, and apply it to define abelianization maps for Galois cohomology of reductive algebraic groups.

18 pages. This is an arXiv version of my old preprint (Princeton 1991 -- Bonn 1992). Since then, Sections 1--3 were covered in the paper of B. Noohi of 2011 written at my request, and Section 4 was covered in my paper of 1998