50 citations · 66 across the 5 of their papers we have counts for
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Homotopy theory of simplicial presheaves in completely decomposable topologies
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 fini…
Unstable motivic homotopy categories in Nisnevich and cdh-topologies
Vladimir Voevodsky
The motivic homotopy categories can be defined with respect to different topologies and different underlying categories of schemes. For a number of reasons (mainly because of the G…
Lectures on motivic cohomology 2000/2001 (written by Pierre Deligne)
Vladimir Voevodsky
These lecture notes cover four topics. There is a proof of the fact that the functors represented by the motivic Eilenberg-Maclane spaces on the motivic homotopy category coincide…
Motives over simplicial schemes
Vladimir Voevodsky
In this paper we define the triangulated category of motives over a simplicial scheme. The morphisms between the Tate objects in this category compute the motivic cohomology of the…
Simplicial radditive functors
Vladimir Voevodsky
The simplicial extension of any functor from Sets to Sets which commutes with directed colimits takes weak equivalences to weak equivalences. The goal of the present paper is const…