Motives over simplicial schemes

Details Motives over simplicial schemes Motives over simplicial schemes

2008-05-28

arxiv.org/abs/0805.4431v1

Mathematics

Algebraic Geometry

Scientific paper

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 underlying scheme. In the last section we consider the special case of "embedded" simplicial schemes, which correspond to the subsheaves of the constant sheaf and naturally appear in the descent problems for motivic cohomology such as the Bloch-Kato conjecture.

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