Combinatorial Descent Data for Gerbes

2011/09/09 by Yekutieli, Amnon · 1 citation
#18G50 (Primary) 18G30 #20L05 (Secondary) #Algebraic Geometry (math.AG) #Algebraic Topology (math.AT) #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1109.1919

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.

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• Nonabelian multiplicative integration and curvature obstructions for surface holonomy

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