Intermediate extension of Chow motives of Abelian type

Abstract

In this article, we give an unconditional construction of a motivic analogue of the intermediate extension in the context of Chow motives of Abelian type. Our main application concerns intermediate extensions of Chow motives associated to Kuga families to the Baily--Borel compactification of a Shimura variety.

83 pages; accepted for publication in Adv. in Math. The results from Section 7 (on realizations) now admit l-adic versions

References in corpus (5)

• Étale motives
• Decomposition de motifs abeliens
• Tate motives and the fundamental group
• On the interior motive of certain Shimura varieties: the case of Picard surfaces
• Mixed motivic sheaves (and weights for them) exist if 'ordinary' mixed motives do

Cited by in corpus (8)

• On torsion pairs, (well generated) weight structures, adjacent $t$-structures, and related (co)homological functors
• Weights and conservativity
• On the intersection motive of certain Shimura varieties: the case of Siegel threefolds
• Equivariant motives and geometric representation theory. (with an appendix by F. Hörmann and M. Wendt)
• The geometric Satake equivalence for integral motives
• Chow motives without projectivity, II
• Motivic Intersection Complex of Certain Shimura varieties
• Absolute intersection motive