Title:
Hypercovers and simplicial presheaves
Authors:
Daniel Dugger
Sharon Hollander
Daniel C. Isaksen
AMS subject classification:
55U35, 18F20
Addresses:
Department of Mathematics, Purdue University
ddugger@math.purdue.edu
Department of Mathematics, University of Chicago
sjh@math.uchicago.edu
Department of Mathematics, University of Notre Dame
isaksen.1@nd.edu
Abstract:
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 the fibrant objects can be
explicitly identified in terms of a hypercover descent
condition. Another is a very simple approach to change-of-site
functors. In an appendix, we discuss how this hypercover localization
compares to the more naive process of localizing at the Cech
complexes; the two are not the same in general, but agree in some
cases of interest.