A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles

Abstract

Let F be the field of rational functions on a smooth projective curve over a finite field, and let π be an unramified cuspidal automorphic representation for PGL2 over F. We prove a variant of the formula of Yun and Zhang relating derivatives of the L-function of π to the self-intersections of Heegner-Drinfeld cycles on moduli spaces of shtukas.In our variant, instead of a self-intersection, we compute the intersection pairing of Heegner-Drinfeld cycles coming from two different quadratic extensions of F, and relate the intersection to the r-th derivative of a product of two toric period integrals.