Mathematical Proceedings of the Cambridge Philosophical Society



Hypercovers and simplicial presheaves


DANIEL DUGGER a1, SHARON HOLLANDER a2 and DANIEL C. ISAKSEN a3
a1 Department of Mathematics, University of Oregon, Eugene, OR 97403, U.S.A. e-mail: ddugger@math.uoregon.edu
a2 Department of Mathematics, University of Chicago, Chicago, IL 60637, U.S.A. e-mail: sjh@math.uchicago.edu
a3 Department of Mathematics, University of Notre Dame, Notre Dame, IN 46556, U.S.A. e-mail: isaksen.1@nd.edu

Article author query
dugger d   [Google Scholar] 
hollander s   [Google Scholar] 
isaksen d   [Google Scholar] 
 

Abstract

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, and the fibrations can be described by a relative descent condition. We give a few applications for this new description of the homotopy theory of simplicial presheaves.

(Received May 27 2002)