Chow motives without projectivity

Details Chow motives without projectivity Chow motives without projectivity

2008-06-20

arxiv.org/abs/0806.3380v2

Compositio Math. 145 (2009), 1196-1226

Mathematics

Algebraic Geometry

38 pages; accepted for publication in Comp. Math

Scientific paper

10.1112/S0010437X0900414X

In paper 0704.4003, Bondarko recently defined the notion of weight structure, and proved that the category $\DgM$ of geometrical motives over a perfect field k, as defined and studied by Voevodsky, Suslin and Friedlander, is canonically equipped with such a structure. Building on this result, and under a condition on the weights avoided by the boundary motive, we describe a method to construct intrinsically in $\DgM$ a motivic version of interior cohomology of smooth, but possibly non-projective schemes. In a sequel to this work, this method will be applied to Shimura varieties.

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