A Gross-Zagier Formula for CM cycles over Shimura Curves

Abstract: In this talk I will introduce my thesis work (in preparation) to prove a Gross-Zagier formula for CM cycles over Shimura curves. The formula connects the global height pairing of special cycles in Kuga varieties over Shimura curves with the derivatives of the L-functions associated to weight-2k modular forms. As a key original ingredient of the proof, I will introduce some harmonic analysis on local systems over graphs, including an explicit construction of Green's function, which we apply to compute some local intersection numbers.

algebraic geometrynumber theory

Audience: researchers in the topic

UCSB Seminar on Geometry and Arithmetic