2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/161889There 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.Algebraic Geometry55U35Homotopy theory of simplicial presheaves in completely decomposable topologiestext