Special Cycle on Shtukas and Categorical Trace

Zeyu Wang

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arXiv · 2509.05526

Special Cycle on Shtukas and Categorical Trace

Zeyu Wang

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Abstract

In this article, we relate the fake special cycle classes $z_{\mathbb{L}_{\sigma},r}$ attached to a Hecke eigensheaf $\mathbb{L}_{\sigma}\in\mathrm{Shv}_{\mathrm{Nilp}}(\mathrm{Bun}_G)$ introduced in the author's previous work to the isotypic part of special cycles on Shtukas. As an application, we relate the self-intersection number of the isotypic part of special cycles arising from Rankin--Selberg period to higher derivatives of Rankin--Selberg $L$-functions.

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Zeyu Wang. 2025-09-05. Special Cycle on Shtukas and Categorical Trace. https://arxiv.org/abs/2509.05526

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