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Chern classes of automorphic bundles (Ben Moonen)

When Apr 18, 2012
from 02:30 PM to 05:00 PM
Where C200 N00.04
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by Ben Moonen (Universiteit van Amsterdam)

Room N00.04

Abstract

I will spend the first part of my talk on an introduction to Shimura varieties, aimed at non-experts. In the second half of my talk I shall discuss tautological classes on compactified Shimura varieties. The picture we have is that for the Shimura variety associated to a pair (G,X) the tautological ring should be isomorphic to the cohomology ring of the compact dual of X, which is a completely explicit ring. We give a simple geometric explanation for this. In cohomology this works. However, on more refined levels (Deligne cohomology, Chow rings) we know this only in special cases and there is a fundamental obstacle that remains. I shall describe where the difficulty lies and will discuss what is known about it.