# On the intersection motive of certain Shimura varieties: the case of Siegel threefolds

## TL;DR

This paper constructs a Hecke-equivariant Chow motive for Siegel threefolds, linking intersection cohomology to motives and enabling the definition of Grothendieck motives for Siegel modular forms.

## Contribution

It introduces a new construction of a Chow motive for Siegel threefolds that captures intersection cohomology and facilitates the study of modular forms through motives.

## Key findings

- Construction of a Hecke-equivariant Chow motive for Siegel threefolds
- Realizations of the motive match intersection cohomology with algebraic coefficients
- Enables the definition of Grothendieck motives for Siegel modular forms

## Abstract

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.