On the interior motive of certain Shimura varieties: the case of Hilbert-Blumenthal varieties

TL;DR

This paper constructs a Hecke-equivariant Chow motive for Hilbert-Blumenthal varieties, whose realizations match their interior cohomology with non-constant algebraic coefficients, advancing understanding of their geometric and arithmetic properties.

Contribution

It introduces a new construction of a Chow motive that captures the interior cohomology of Hilbert-Blumenthal varieties with algebraic coefficients, linking motives and intersection cohomology.

Findings

Construction of a Hecke-equivariant Chow motive for Hilbert-Blumenthal varieties

Realizations of the motive match interior cohomology with algebraic coefficients

Enhances understanding of the motive-cohomology relationship in arithmetic geometry

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.