### Homotopy theory of simplicial sheaves in completely decomposable topologies, by Vladimir Voevodsky

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.

Vladimir Voevodsky <vladimir@ias.edu>