Chow motives without projectivity

Abstract

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.

38 pages; accepted for publication in Comp. Math

References in corpus (2)

• Differential graded motives: weight complex, weight filtrations and spectral sequences for realizations; Voevodsky vs. Hanamura
• The boundary motive: definition and basic properties

Cited by in corpus (11)

• Weight structures vs. $t$-structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
• Decomposition de motifs abeliens
• On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
• Z[1/p]-motivic resolution of singularities
• Intermediate extension of Chow motives of Abelian type
• On the interior motive of certain Shimura varieties: the case of Picard surfaces
• Non-commutative localizations of additive categories and weight structures; applications to birational motives
• Regulators for Rankin-Selberg products of modular forms
• On the intersection motive of certain Shimura varieties: the case of Siegel threefolds
• Degeneration of Hodge structures over Picard modular surfaces
• Chow motives without projectivity, II