### Hypercovers and simplicial presheaves, by Daniel Dugger, Sharon Hollander, and Daniel C. Isaksen

We use hypercovers to study the homotopy theory of simplicial
presheaves. The main result says that model structures for simplicial
presheaves involving local weak equivalences can be constructed by
localizing at the hypercovers. One consequence is that the fibrant
objects can be explicitly described in terms of a hypercover descent
condition. These ideas are central to constructing realization
functors on the homotopy theory of schemes. We give a
few other applications for this new description of the homotopy theory
of simplicial presheaves.

Daniel Dugger <ddugger@math.purdue.edu>

Sharon Hollander <sjh@math.uchicago.edu>

Daniel C. Isaksen <isaksen.1@nd.edu>