Non-reductive special cycles and Twisted Arithmetic Fundamental Lemma
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arXiv
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929371076362240 |
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| author | Zhang, Zhiyu |
| author_facet | Zhang, Zhiyu |
| contents | We consider arithmetic analogs of the relative Langlands program and applications of new non-reductive geometry. Firstly, we introduce mirabolic special cycles, which produce special cycles on many Hodge type Rapoport-Zink spaces via pullbacks e.g. Kudla--Rapoport cycles. Secondly, we formulate arithmetic intersection problems for these cycles and formulate a method of arithmetic induction. As a main example, we formulate arithmetic twisted Gan--Gross--Prasad conjectures on unitary Shimura varieties and prove a key twisted arithmetic fundamental lemma using mirabolic special cycles, arithmetic inductions, and Weil type relative trace formulas. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2406_00986 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Non-reductive special cycles and Twisted Arithmetic Fundamental Lemma Zhang, Zhiyu Number Theory Algebraic Geometry Representation Theory 11F67, 11G40, 14G35 We consider arithmetic analogs of the relative Langlands program and applications of new non-reductive geometry. Firstly, we introduce mirabolic special cycles, which produce special cycles on many Hodge type Rapoport-Zink spaces via pullbacks e.g. Kudla--Rapoport cycles. Secondly, we formulate arithmetic intersection problems for these cycles and formulate a method of arithmetic induction. As a main example, we formulate arithmetic twisted Gan--Gross--Prasad conjectures on unitary Shimura varieties and prove a key twisted arithmetic fundamental lemma using mirabolic special cycles, arithmetic inductions, and Weil type relative trace formulas. |
| title | Non-reductive special cycles and Twisted Arithmetic Fundamental Lemma |
| topic | Number Theory Algebraic Geometry Representation Theory 11F67, 11G40, 14G35 |
| url | https://arxiv.org/abs/2406.00986 |