Weights and conservativity

The purpose of this article is to study conservativity in the context of triangulated categories equipped with a weight structure. As application, we establish (weight) conservativity for the restriction of the (generic) l-adic realization to the category of motives of Abelian type of characteristic zero.Comment: 22 pages; only few changes wrt. last version except for the numbering of the sections, which is now compatible with the published versio

On the intersection motive of certain Shimura varieties: the case of Siegel threefolds

In this article, we construct a Hecke-equivariant Chow motive whose realizations equal intersection cohomology of Siegel threefolds with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Siegel modular forms.Comment: 36 pages; accepted for publication in Annals of K-Theory. Following remarks of the referee, the proof of Cor. 1.13 is now more detaile

On the interior motive of certain Shimura varieties: the case of Picard surfaces

The purpose of this article is to construct a Hecke-equivariant Chow motive whose realizations equal interior (or intersection) cohomology of Picard surfaces with regular algebraic coefficients. As a consequence, we are able to define Grothendieck motives for Picard modular forms.Comment: 34 pages; accepted for publication in manuscripta mathematica. arXiv admin note: text overlap with arXiv:0906.423

Motivic intersection complex

In this article, we give an unconditional definition of the motivic analogue of the intersection complex, establish its basic properties, and prove its existence in certain cases.Comment: 28 pages; final version. Following the request of the referee, the relation between realizations of the intersection complex and intersection cohomology was addresse

The boundary motive: definition and basic properties

We introduce the notion of the boundary motive of a scheme X over a perfect field. By definition, it measures the difference between the motive X and the motive with compact support of X. We develop three tools to compute the boundary motive in terms of the geometry of a compactification of X: co-localization, invariance under abstract blow-up, and analytical invariance. We then prove auto-duality of the boundary motive of a smooth scheme X. As a formal consequence of this, and of co-localization, we obtain a fourth computational tool, namely localization for the boundary motive.Comment: 33 pages; accepted for publication in Comp. Math. Following the request of the referee, a section on the case of normal crossings was adde