Heegner-Drinfeld cycles and a higher Gross-Zagier formula at deeper level

Abstract: By work of Yun-Zhang the self-intersection number of Heegner-Drifeld cycles on moduli spaces of shtukas at Iwahori-level is related to (higher) derivatives of certain $L$-functions, providing a vast generalization of the Gross-Zagier formula in the function field setting.

In this talk, I will discuss integral models for certain deeper level structures (like arbitrary, i.e. possibly deeper than Iwahori, $\Gamma_0(\Sigma)$-level) and explain how to construct Heegner-Drinfeld cycles on them in order to formulate a generalization of the higher GZ-formula.

This is partially based on joint work in progress with Zhiwei Yun.

algebraic geometrynumber theory

Audience: researchers in the topic

MIT number theory seminar

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