24 research outputs found
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
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
On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
The purpose of this article is to construct a Hecke-equivariant Chow motive
whose realizations equal interior (or intersection) cohomology of
Hilbert-Blumenthal varieties with non-constant algebraic coefficients.Comment: 31 pages; no changes wrt. last version except for the numbering of
the sections, which is now compatible with the published versio
Shimura data and corners: topology
The purpose of this article is to give a new construction of the map relating
the Borel-Serre and the Baily-Borel compactifications of a Shimura variety
(Zucker 1983), and to provide a close analysis of its main properties.Comment: 97 pages; minor changes since the first version, in order to optimize
presentation of the companion paper [W