|Date: Thursday, January 08, 2015
Location: 4088 East Hall (5:00 PM to 6:00 PM)
Title: Congruences between Abel-Jacobi images of generalized Heegner cycles and special values of p-adic L-functions
Abstract: I will discuss my result proving a congruence between the Bertolini-Darmon-Prasanna anticyclotomic p-adic L-function attached to a newform f with reducible residual p-adic Galois representation and Katz's p-adic L-function. Using the p-adic Waldspurger formula of Bertolini-Darmon-Prasanna, there follows a congruence between the image under the p-adic Abel-Jacobi map of a generalized Heegner cycle and a special value of the Katz p-adic L-function, which can be explicitly evaluated. I will frame my discussion in the context of the Beilinson-Bloch conjectures and Deligne-Scholl motives. As an example, I will discuss the weight 2 case, and applications to the arithmetic of elliptic curves.
Speaker: Daniel Kriz
Institution: Princeton University