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Characterizing algebraic stacks

Author: Sharon Hollander
Journal: Proc. Amer. Math. Soc. 136 (2008), 1465-1476
MSC (2000): Primary 55U10; Secondary 18G55, 14A20
Published electronically: December 6, 2007
MathSciNet review: 2367121
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Abstract: We extend the notion of algebraic stack to an arbitrary subcanonical site $ \EuScript C$. If the topology on $ \EuScript C$ is local on the target and satisfies descent for morphisms, we show that algebraic stacks are precisely those which are weakly equivalent to representable presheaves of groupoids whose domain map is a cover. This leads naturally to a definition of algebraic $ n$-stacks. We also compare different sites naturally associated to a stack.

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Additional Information

Sharon Hollander
Affiliation: Department of Mathematics, Hebrew University, Jerusalem, Israel
Address at time of publication: Centro de Análise Mathematica, Geometria e Sistemas Dinâmicos, Instituto Superior Técnico, Tech. Univ. Lisbon, Portugal

Received by editor(s): May 30, 2006
Received by editor(s) in revised form: June 29, 2006
Published electronically: December 6, 2007
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.