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Abstract:
We will look at cycle classes on a higher dimensional generalization
of an universal elliptic curve over a modular curve. The universal elliptic
curve will be replaced by a universal 9-dimensional abelian scheme
with additional structure and the generalization of a modular curve is
given by a Shimura variety.
We will in particular show that these universal abelian schemes viewed
as schemes over an algebraically closed field satisfy a strengthening
(conjectured by J. Murre) of Grothendieck's Standard Conjecture C.
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