Chern classes of automorphic bundles

• Applicant: Professorin Dr. Hélène Esnault
• Subject Area: Mathematics
• Term: from 2018 to 2022
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 403681677

Our aim is threefold. The basic objects are non-proper Shimura varieties (embeddable in the Siegel space), automorphic bundles, their various Chern classes over compactifications of the Shimura varieties. The goals:1) Construct Chern classes of automorphic vector bundles in l-adic cohomology of the minimal compactification of a Shimura variety over barQ.2) Try to understand in which more arithmetic cohomology it is possible to lift those l-adic Chern classes.3) If 1) and 2) were available, one could try to construct the l-adic realization of themotivic mixed Tate extensions which are believed by many people to exist.

• DFG Programme: Priority Programmes
• Subproject of: SPP 1786: Homotopy Theory and Algebraic Geometry