Algebraic Cycles on Picarad Moduli Spaces of Abelian Varieties

Algebraic Cycles on Picarad Moduli Spaces of Abelian Varieties - Michael Rapoport

Michael Rapoport
University of Bonn
November 11, 2010

Picard moduli spaces parametrize principally polarized abelian varieties with complex multiplication by the ring of integers in an imaginary-quadratic field. The loci where the abelian varieties split off an elliptic curve in a controlled way are divisors on this moduli space. We study the intersection behaviour of these divisors and prove in the non-degenerate case a relation between their intersection numbers and Fourier coefficients of the derivative at s=0 of a certain incoherent Eisenstein series for the unitary group. This is joint work with Kudla.