Ignacio Muñoz Jiménez: Gross points in ordinary families of Hilbert modular forms

Number Theory Seminar: Ignacio Muñoz Jiménez (University of Genova)

Gross points in ordinary families of Hilbert modular forms

The Gross--Zagier formula provides a fundamental link between central derivatives of L-functions and Heegner points on indefinite Shimura curves. In this talk, I will focus on the other side of the picture: the arithmetic of definite quaternion algebras and definite Shimura varieties. In this setting, I will explain how Gross points, the counterpart of Heegner points, can be used to construct an anticyclotomic p-adic L-function. I will then discuss how this construction interpolates in Hida families of modular forms, and I will conclude with a review of recent work extending these ideas to the totally real setting.