14 citations · 23 across the 5 of their papers we have counts for
5 papers
Characterizing algebraic stacks
Sharon Hollander
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…
Descent for quasi-coherent sheaves on stacks
Sharon Hollander
We give a homotopy theoretic characterization of sheaves on a stack and, more generally, a presheaf of groupoids on an arbitary small site C. We use this to prove homotopy invarian…
Realizing modules over the homology of a DGA
Gustavo Granja, Sharon Hollander
Let A be a DGA over a field and X a module over H_*(A). Fix an -structure on H_*(A) making it quasi-isomorphic to A. We construct an equivalence of categories between A_{…
Hypercovers and simplicial presheaves
Daniel Dugger, Sharon Hollander, Daniel C. Isaksen
We prove that Jardine's model category of simplicial presheaves can be obtained by localizing the `discrete' version at the collection of all hypercovers. One consequence is that t…
A Homotopy Theory for Stacks
Sharon Hollander
We give a homotopy theoretic characterization of stacks on a site $\cC$ as the {\it homotopy sheaves} of groupoids on $\cC$. We use this characterization to construct a model categ…