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arXiv · 1707.00213

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

Benjamin Howard·Ari Shnidman
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Abstract

Let $F$ be the field of rational functions on a smooth projective curve over a finite field, and let $\pi$ be an unramified cuspidal automorphic representation for $\mathrm{PGL}_2$ over $F$. We prove a variant of the formula of Yun and Zhang relating derivatives of the $L$-function of $\pi$ 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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Benjamin Howard, Ari Shnidman. 2017-07-01. A Gross-Kohnen-Zagier formula for Heegner-Drinfeld cycles. https://arxiv.org/abs/1707.00213

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