Combinatorial Descent Data for Gerbes

TL;DR

This paper studies descent data in cosimplicial crossed groupoids, providing a combinatorial framework that models gerbes in algebraic geometry, and shows that weak equivalences induce bijections on gauge classes.

Contribution

It introduces a combinatorial abstraction for gerbe descent data and proves a key invariance property under weak equivalences.

Findings

Weak equivalences induce bijections on gauge equivalence classes

Provides a combinatorial model for descent data of gerbes

Bridges algebraic geometry and combinatorial groupoid theory

Abstract

We consider descent data in cosimplicial crossed groupoids. This is a combinatorial abstraction of the descent data for gerbes in algebraic geometry. The main result is this: a weak equivalence between cosimplicial crossed groupoids induces a bijection on gauge equivalence classes of descent data.