Characterizing algebraic stacks

Details Characterizing algebraic stacks Characterizing algebraic stacks

2007-08-20

arxiv.org/abs/0708.2705v1

Mathematics

Algebraic Topology

12 pages, to appear in Proc. Amer. Math. Soc

Scientific paper

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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