Intermediate extension of Chow motives of Abelian type

TL;DR

This paper constructs an unconditional motivic analogue of the intermediate extension for Chow motives of Abelian type, with applications to extending motives over Shimura varieties.

Contribution

It introduces a new unconditional construction of the intermediate extension in the setting of Chow motives of Abelian type, extending motives over compactifications.

Findings

Constructed an unconditional motivic intermediate extension.

Applied the construction to Kuga families and Shimura varieties.

Extended Chow motives to Baily--Borel compactifications.

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.