Homotopy theory of simplicial presheaves in completely decomposable topologies

Details Homotopy theory of simplicial presheaves in completely decomposable topologies Homotopy theory of simplicial presheaves in completely decomposable topologies

2008-05-29

arxiv.org/abs/0805.4578v1

Mathematics

Algebraic Geometry

Scientific paper

There are two approaches to the homotopy theory of simplicial (pre-)sheaves. One developed by Joyal and Jardine works for all sites but produces a model structure which is not finitely generated even in the case of sheaves on a Noetherian topological space. The other one developed by Brown and Gersten gives a nice model structure for sheaves on a Noetherian space of finite dimension but does not extend to all sites. In this paper we define a class of sites for which a generalized version of the Brown-Gersten approach works.

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