Characterizing algebraic stacks

Sharon Hollander

doi:10.1090/S0002-9939-07-08832-6

Characterizing algebraic stacks

Sharon Hollander

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

We extend the notion of algebraic stack to an arbitrary subcanon- ical site C. If the topology on 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 ri-stacks. We also compare different sites naturally associated to a stack.

Original language	English
Pages (from-to)	1465-1476
Number of pages	12
Journal	Proceedings of the American Mathematical Society
Volume	136
Issue number	4
DOIs	https://doi.org/10.1090/S0002-9939-07-08832-6
State	Published - 1 Apr 2008
Externally published	Yes

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9939-07-08832-6

Cite this

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AB - We extend the notion of algebraic stack to an arbitrary subcanon- ical site C. If the topology on 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 ri-stacks. We also compare different sites naturally associated to a stack.

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Characterizing algebraic stacks

Abstract

ASJC Scopus subject areas

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