Homotopy theory of simplicial sheaves in completely decomposable topologies

By Vladimir Voevodsky. 2008

109 citations recorded by the source corpus.

Abstract 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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/aee7386a14d903713d6b166506a33ae7da0ceb29

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

T-motives (2016, background): “Assuming that ∅ → X is inM for each object X of C we denote hn(X) := hn(X, ∅) the associated sorts for n ∈ Z. Assume that C or a category C′/X of triangles over an object X of C is endowed with a cd-structure in the sense of Voevodsky [31].”
Triangulated Categories of Mixed Motives (2009, unknown): “Recall from [Voe00a] that a cd-structure on S is a collection P of commutative squares of schemes B // Q Y f A e // X which is closed under isomorphisms.”
Unstable motivic homotopy categories in Nisnevich and cdh-topologies (2008, methodology): “Let C be a category with a complete regular bounded cd-structure P (see [9]) and an interval I (see [7, Section 2.”