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arXiv · 0708.2705

Characterizing algebraic stacks

Sharon Hollander
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Abstract

We extend the notion of algebraic stack to an arbitrary subcanonical 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 n-stacks. We also compare different sites naturally associated to a stack.

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Sharon Hollander. 2007-08-20. Characterizing algebraic stacks. https://arxiv.org/abs/0708.2705

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