#### Volume 7, issue 1 (2007)

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Descent for quasi-coherent sheaves on stacks

### Sharon Hollander

Algebraic & Geometric Topology 7 (2007) 411–437
##### Abstract

We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site $\mathsc{C}$. We use this to prove homotopy invariance and generalized descent statements for categories of sheaves and quasi-coherent sheaves. As a corollary we obtain an alternate proof of a generalized change of rings theorem of Hovey.

##### Keywords
stacks, descent, quasi-coherent sheaves
##### Mathematical Subject Classification 2000
Primary: 14A20
Secondary: 18G55, 55U10
##### Publication
Received: 30 June 2006
Revised: 10 November 2006
Accepted: 12 December 2006
Published: 25 April 2007
##### Authors
 Sharon Hollander Department of Mathematics Hebrew University Jerusalem Israel Center for Mathematical Analysis, Geometry, and Dynamical Systems Instituto Superior Técnico Universidade Técnica de Lisboa Lisbon Portugal