On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties
arXiv:0906.4239 · doi:10.1093/imrn/rnr109
Abstract
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.
31 pages; no changes wrt. last version except for the numbering of the sections, which is now compatible with the published version
References in corpus (8)
- Weight structures vs. -structures; weight filtrations, spectral sequences, and complexes (for motives and in general)
- Chow motives without projectivity
- Notes on Artin-Tate motives
- L-modules and the Conjecture of Rapoport and Goresky-MacPherson
- The boundary motive: definition and basic properties
- Pure motives, mixed motives and extensions of motives associated to singular surfaces
- Boundary motive, relative motives and extensions of motives
- On the boundary motive of a Shimura variety
Cited by in corpus (11)
- Decomposition de motifs abeliens
- Euler systems for Hilbert modular surfaces
- Intermediate extension of Chow motives of Abelian type
- On the interior motive of certain Shimura varieties: the case of Picard surfaces
- On the intersection motive of certain Shimura varieties: the case of Siegel threefolds
- Boundary motive, relative motives and extensions of motives
- On the interior motive of certain Shimura varieties : the case of Picard varieties
- Degeneration of Hodge structures over Picard modular surfaces
- Chow motives without projectivity, II
- Absolute intersection motive
- Motivic Intersection Complex of Certain Shimura varieties