Special Cycle on Shtukas and Categorical Trace

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.

arXiv comment61 pages, comments welcome!