Extensions of the Gross-Zagier formula

Extensions of the Gross-Zagier formula

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Kartik Prasanna, University of Michigan
IAS Room S-101

I will first discuss the general conjectural picture relating algebraic cycles to L-functions and some extensions of the Gross-Zagier formula involving p-adic L-functions. This leads naturally to the question of constructing algebraic cycles corresponding to the vanishing of certain Rankin-Selberg L-functions at the center of symmetry. Finally, I will outline some new constructions of such cycles, based on work in progress with A. Ichino.