# Chern classes of automorphic vector bundles

## TL;DR

This paper proves that the Chern classes of automorphic vector bundles on certain Shimura varieties are rationally trivial, supporting Beilinson's conjectures about their vanishing in Chow groups.

## Contribution

It establishes the rational triviality of Chern classes in continuous ll-adic cohomology for automorphic bundles on projective Shimura varieties, confirming a key aspect of Beilinson's conjectures.

## Key findings

- Chern classes are rationally trivial in continuous ll-adic cohomology.
- Supports Beilinson's conjecture on Chow group vanishing.
- Provides a cohomological proof for automorphic vector bundles.

## Abstract

We prove that Chern classes in continuous $\ell$-adic cohomology of automorphic bundles associated to representations of $G$ on a projective Shimura variety with data $(G,X)$ are trivial rationally. It is a consequence of Beilinson's conjectures which predict that the Chern classes in the Chow groups vanish rationally.