A Gross-Zagier Formula for CM cycles over Shimura Curves

Abstract: In this talk I will introduce my thesis work in progress 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.

number theory

Audience: researchers in the topic

UCLA Number Theory Seminar