Descent for quasi-coherent sheaves on stacks

Hollander, Sharon¹

¹Department of Mathematics, Hebrew University, Jerusalem, Israel, Center for Mathematical Analysis, Geometry, and Dynamical Systems, Instituto Superior Técnico, Universidade Técnica de Lisboa, Lisbon, Portugal

Algebraic and Geometric Topology, Tome 7 (2007) no. 1, pp. 411-437

Résumé

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.

Détail

DOI : 10.2140/agt.2007.7.411

Keywords: stacks, descent, quasi-coherent sheaves

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