Characterizing algebraic stacks

Hollander, Sharon

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

Characterizing algebraic stacks
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by Sharon Hollander

Proc. Amer. Math. Soc. 136 (2008), 1465-1476

DOI: https://doi.org/10.1090/S0002-9939-07-08832-6

Published electronically: December 6, 2007

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Abstract:

We extend the notion of algebraic stack to an arbitrary subcanonical site $\mathcal C$. If the topology on $\mathcal C$ 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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