Manin-Mumford in arithmetic pencils
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
| Published: |
2021
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| _version_ | 1866910344385921024 |
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| author | Baldi, Gregorio Richard, Rodolphe Ullmo, Emmanuel |
| author_facet | Baldi, Gregorio Richard, Rodolphe Ullmo, Emmanuel |
| contents | We obtain a refinement of Manin-Mumford (Raynaud's Theorem) for abelian schemes over some ring of integers. Torsion points are replaced by special 0-cycles, that is reductions modulo some, possibly varying, prime of Galois orbits of torsion points. There is a flat/horizontal part and a vertical one. The irreducible components of the flat part are given by the Zariski closure, over the integers, of torsion cosets of the generic fibre of the abelian scheme. The vertical components are given by translates of abelian subvarieties, which 'come from characteristic zero'. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2105_12027 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Manin-Mumford in arithmetic pencils Baldi, Gregorio Richard, Rodolphe Ullmo, Emmanuel Number Theory Algebraic Geometry We obtain a refinement of Manin-Mumford (Raynaud's Theorem) for abelian schemes over some ring of integers. Torsion points are replaced by special 0-cycles, that is reductions modulo some, possibly varying, prime of Galois orbits of torsion points. There is a flat/horizontal part and a vertical one. The irreducible components of the flat part are given by the Zariski closure, over the integers, of torsion cosets of the generic fibre of the abelian scheme. The vertical components are given by translates of abelian subvarieties, which 'come from characteristic zero'. |
| title | Manin-Mumford in arithmetic pencils |
| topic | Number Theory Algebraic Geometry |
| url | https://arxiv.org/abs/2105.12027 |