Pure and Applied Mathematics Quarterly

Volume 13 (2017)

Number 2

Special Issue in Honor of Yuri Manin: Part 2 of 2

Guest Editors: Lizhen Ji, Kefeng Liu, Yuri Tschinkel, and Shing-Tung Yau

Chern classes of automorphic vector bundles

Pages: 193 – 213

DOI: https://dx.doi.org/10.4310/PAMQ.2017.v13.n2.a1


Hélène Esnault (Mathematik, Freie Universität Berlin, Germany)

Michael Harris (Department of Mathematics, Columbia University, New York, N.Y., U.S.A.)


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.

The research leading to these results has received funding from the European Research Council under the European Community’s Seventh Framework Programme (FP7/2007-2013)/ERC Advanced Grants 22224001 and 290766 (AAMOT), the Einstein Foundation, the NSF grant DMS-1404769.

Received 31 January 2017

Published 14 September 2018