We give a homotopy theoretic characterization of stacks on a site C as the homotopy sheaves of groupoids on C. We use this characterization to construct a model category in which stacks are theâ€¦ (More)

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 invariance and generalizedâ€¦ (More)

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 areâ€¦ (More)

The purpose of this paper is to give a new presentation of some of the main results concerning Landweber exactness in the context of the homotopy theory of stacks. We present two new criteria forâ€¦ (More)

Let I be a small indexing category, G : I â†’ Cat be a functor and BG âˆˆ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicialâ€¦ (More)

Let I be a small indexing category, G : I â†’ Cat be a functor and BG âˆˆ Cat denote the Grothendieck construction on G. We define and study Quillen pairs between the category of diagrams of simplicialâ€¦ (More)

In this paper we construct a pushforward-pullback adjoint pair for categories of quasi-coherent sheaves, along a morphism of algebraic stacks, which is represented in algebraic stacks over the site Câ€¦ (More)

We use obstruction theory based on the unstable Adams spectral sequence for S3 to study the classification of quaternionic line bundles over finite dimensional complexes. We pay special attention toâ€¦ (More)

Let A be a DGA over a field and X a module over Hâˆ—(A). Fix an Aâˆž-structure on Hâˆ—(A) making it quasi-isomorphic to A. We construct an equivalence of categories between An+1-module structures on X andâ€¦ (More)