More regular formal moduli spaces and arithmetic transfer conjectures: the ramified quadratic case
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2025
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| _version_ | 1866912460312674304 |
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| author | Luo, Yu Rapoport, Michael Zhang, Wei |
| author_facet | Luo, Yu Rapoport, Michael Zhang, Wei |
| contents | For unitary groups associated to a ramified quadratic extension of a $p$-adic field, we define various regular formal moduli spaces of $p$-divisible groups with parahoric levels, characterize exceptional special divisors on them, and construct correspondences between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in this context. We prove the conjectures in the lowest dimensional cases. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2507_01395 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | More regular formal moduli spaces and arithmetic transfer conjectures: the ramified quadratic case Luo, Yu Rapoport, Michael Zhang, Wei Number Theory Algebraic Geometry Representation Theory For unitary groups associated to a ramified quadratic extension of a $p$-adic field, we define various regular formal moduli spaces of $p$-divisible groups with parahoric levels, characterize exceptional special divisors on them, and construct correspondences between them. We formulate arithmetic transfer conjectures, which are variants of the arithmetic fundamental lemma conjecture in this context. We prove the conjectures in the lowest dimensional cases. |
| title | More regular formal moduli spaces and arithmetic transfer conjectures: the ramified quadratic case |
| topic | Number Theory Algebraic Geometry Representation Theory |
| url | https://arxiv.org/abs/2507.01395 |