Manin-Drinfeld cycles and L-functions

Abstract: I'll describe a formula I proved a few years ago relating the derivative of an L-function of an automorphic representation for PGL_2 over a function field to an intersection pairing of two special algebraic cycles in a moduli space of shtukas. The proof, which I will try to sketch, is via the geometric relative trace formula of Jacquet-Yun-Zhang. The formula leads to interesting questions about Manin-Drinfeld cycles, which are generalizations of the cusps on modular curves, as I will explain.

number theory

Audience: researchers in the discipline

Algebra and Number Theory Seminars at Université Laval