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

2017/07/01 by Howard, Benjamin, Shnidman, Ari · 1 citation
#11F67 #14C25 #14G10 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1707.00213

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.

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