Chow motives without projectivity

Jörg Wildeshaus (1)

1 LAGA - Laboratoire Analyse, Géométrie et Applications

In paper 0704.4003, Bondarko recently defined the notion of weight structure, and proved that the category DgM of geometrical motives, 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.

Mots clés: weight structures; weight filtrations; Chow motives; geometrical motives; motives for modular forms; boundary motive; interior motive

Domaines: Géométrie algébrique [math.AG]; K-théorie et homologie [math.KT]

Jörg Wildeshaus. Chow motives without projectivity. Compositio Mathematica, 2009, 145, pp.1196-1226. ⟨10.1112/S0010437X0900414X⟩. ⟨hal-00290944⟩