Quasi-abelian crossed modules and nonabelian cohomology

TL;DR

This paper extends nonabelian Galois cohomology theory for algebraic groups from number fields to general base schemes, providing new insights into their arithmetic over global function fields.

Contribution

It generalizes Borovoi's work to broader base schemes, advancing the understanding of nonabelian cohomology in algebraic geometry.

Findings

New results on the arithmetic of reductive groups over global function fields

Extension of nonabelian Galois cohomology to general base schemes

Broader applicability of cohomological methods in algebraic groups

Abstract

We extend the work of M.Borovoi on the nonabelian Galois cohomology of linear reductive algebraic groups over number fields to a general base scheme. As an application, we obtain new results on the arithmetic of such groups over global function fields.