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Hypercovers and simplicial presheaves

Published online by Cambridge University Press:  15 January 2004

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

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.

Type
Research Article
Copyright
2004 Cambridge Philosophical Society

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