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

Authors

Hélène Esnault (Mathematik, Freie Universität Berlin, Germany)

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

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.

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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