Date: Thursday, January 08, 2015
Location: 4088 East Hall (5:00 PM to 6:00 PM)
Title: Congruences between AbelJacobi images of generalized Heegner cycles and special values of padic Lfunctions
Abstract: I will discuss my result proving a congruence between the BertoliniDarmonPrasanna anticyclotomic padic Lfunction attached to a newform f with reducible residual padic Galois representation and Katz's padic Lfunction. Using the padic Waldspurger formula of BertoliniDarmonPrasanna, there follows a congruence between the image under the padic AbelJacobi map of a generalized Heegner cycle and a special value of the Katz padic Lfunction, which can be explicitly evaluated. I will frame my discussion in the context of the BeilinsonBloch conjectures and DeligneScholl motives. As an example, I will discuss the weight 2 case, and applications to the arithmetic of elliptic curves.
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Speaker: Daniel Kriz
Institution: Princeton University
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