Characterizing algebraic stacks
Abstract
Description
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.
12 pages, to appear in Proc. Amer. Math. Soc
12 pages, to appear in Proc. Amer. Math. Soc