Gerbes for the Chow

TL;DR

This paper simplifies the complex theory of non-Abelian cohomology using gerbes, and applies it to higher divisors and Chow theory, advancing the mathematical understanding of these concepts.

Contribution

It introduces a simplified approach to non-Abelian cohomology via gerbes and demonstrates its application to higher divisors and Chow theory.

Findings

Simplified the framework for non-Abelian cohomology using gerbes

Applied the theory to higher divisors in algebraic geometry

Extended the approach to Chow theory

Abstract

Finding coherent relations to define non Abelian cohomology is a thriller which entertains the mathematical community since fifty one years. The purpose of this paper is to simplify the attempt to beat it defined by the author which used the notion of sequences of fibred categories and to apply the resulting theory to higher divisors and Chow theory.