Date: Monday, April 22, 2013
Location: 4096 East Hall (4:10 PM to 5:00 PM)
Title: Generalized Heegner cycles, Shimura curves, and special values of p-adic L-functions
Abstract: The Gross-Zagier formula relates special values of the derivative of a Rankin-Selberg L-function to heights of "Heegner points" on elliptic curves. The existence of these points requires an arithmetic assumption (the "Heegner hypothesis"), but Zhang established an analogue with this assumption dropped. The geometric object of interest in Zhang's work is a compact quotient of the upper half plane called a Shimura curve. We give a p-adic formula which relates a p-adic logarithm of a Heegner cycle on a variety fibered over a Shimura curve to special values of a p-adic L-function, removing the Heegner hypothesis from work of Bertolini, Darmon, and Prasanna over modular curves. This formula follows from a "q-expansion-free" approach to p-adic modular forms coming from the deformation theory of ordinary abelian varieties in characteristic p.
Speaker: Hunter Brooks
Institution: UM
Event Organizer: mityab@umich.edu
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