A remark on the paper of Deninger and Murre

TL;DR

This paper demonstrates that Deninger and Murre's results imply the torsion property of Chern classes in the Chow ring for de Rham bundles of abelian schemes, connecting to later proofs by van der Geer.

Contribution

It shows how existing results by Deninger and Murre imply the torsion nature of Chern classes, providing insights into their orders and relations.

Findings

Chern classes of de Rham bundles are torsion in the Chow ring

Results by Deninger and Murre imply torsion property

Discussion on the orders of these classes

Abstract

We show that the results proven by Deninger and Murre directly imply that the Chern classes of the de Rham bundle of an abelian scheme are torsion elements in the Chow ring, a result that was later proven by van der Geer. We also discuss several results about the orders of these classes.