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This is a Quantitative Study study.

October 3, 2025Open Access

Special Cycle on Shtukas and Categorical Trace

Puntos clave

A connection exists between special cycle classes and the isotypic part of special cycles in Shtukas, enhancing understanding of their relationships.
The self-intersection number of special cycles relates to higher derivatives of Rankin-Selberg L-functions, featuring crucial implications.
Investigating special cycle classes broadens the framework for analyzing L-functions in a new context.
The findings may lead to deeper insights in the theory of automorphic forms and number theory.

Resumen

In this article, we relate the fake special cycle classes z₋_⏢, ₑ attached to a Hecke eigensheaf L_σ₍₈₋₏ (BunG) 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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Cite This Study

Zeyu Wang (Fri,) studied this question.

synapsesocial.com/papers/68e034f7f0e39f13e7fa302c https://doi.org/https://doi.org/10.48550/arxiv.2509.05526

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