A Gross-Kohnen-Zagier type formula for moduli of shtukas with Iwahori level structures

TL;DR

This paper extends the Gross-Kohnen-Zagier formula to the setting of moduli of shtukas with Iwahori level structures, relating intersection numbers of Heegner-Drinfeld cycles to period integrals.

Contribution

It introduces a new formula connecting intersection numbers of cycles on moduli stacks with Iwahori level structures, generalizing previous results to this more complex setting.

Findings

Intersection number relates to a specific period integral.

Extension of Howard-Shinidman's result to Iwahori level structures.

Provides new insights into the geometry of shtukas with level structures.

Abstract

In this paper I'm going to study the intersection of two Heegner-Drinfeld cycles coming from two different nonsplit tori on the Yun-Zhang moduli stack of $PGL_2$ Drinfeld stukas with Iwahori level structure. We will see that the intersection number is related to a certain period integral. It is an extension of the result by Howard-Shinidman to the Iwahori case.