Descent for quasi-coherent sheaves on stacks

Hollander, Sharon

doi:10.2140/agt.2007.7.411

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Descent for quasi-coherent sheaves on stacks

Sharon Hollander

Algebraic & Geometric Topology 7 (2007) 411–437

DOI: 10.2140/agt.2007.7.411

Abstract

We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site $C$ . 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

References

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

Volume 7, issue 1 (2007)