Project description

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 the motivic mixed Tate extensions which are believed by many people to exist.

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