Special Cycle on Shtukas and Categorical Trace
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arXiv
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866908522170548224 |
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| author | Wang, Zeyu |
| author_facet | Wang, Zeyu |
| contents | In this article, we relate the fake special cycle classes $z_{\mathbb{L}_σ,r}$ attached to a Hecke eigensheaf $\mathbb{L}_σ\in\mathrm{Shv}_{\mathrm{Nilp}}(\mathrm{Bun}_G)$ 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2509_05526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Special Cycle on Shtukas and Categorical Trace Wang, Zeyu Number Theory Algebraic Geometry Representation Theory In this article, we relate the fake special cycle classes $z_{\mathbb{L}_σ,r}$ attached to a Hecke eigensheaf $\mathbb{L}_σ\in\mathrm{Shv}_{\mathrm{Nilp}}(\mathrm{Bun}_G)$ 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. |
| title | Special Cycle on Shtukas and Categorical Trace |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2509.05526 |