Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors
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arXiv
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| Auteurs principaux: | , , , , |
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| Format: | Preprint |
| Publié: |
2023
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| _version_ | 1866914824177319936 |
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| author | Ganatra, Sheel Hanlon, Andrew Hicks, Jeff Pomerleano, Daniel Sheridan, Nick |
| author_facet | Ganatra, Sheel Hanlon, Andrew Hicks, Jeff Pomerleano, Daniel Sheridan, Nick |
| contents | We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirror symmetry. We also prove homological mirror symmetry for Greene--Plesser mirror pairs in all characteristics such that the B-side family has good reduction, generalizing work of the fifth author and Smith over the complex numbers. A key technical ingredient is a new versality argument which allows us to work throughout over a Novikov-type ring with integer coefficients. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2312_01949 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors Ganatra, Sheel Hanlon, Andrew Hicks, Jeff Pomerleano, Daniel Sheridan, Nick Symplectic Geometry Algebraic Geometry Number Theory We prove the `integrality of Taylor coefficients of mirror maps' conjecture for Greene--Plesser mirror pairs as a natural byproduct of an arithmetic refinement of homological mirror symmetry. We also prove homological mirror symmetry for Greene--Plesser mirror pairs in all characteristics such that the B-side family has good reduction, generalizing work of the fifth author and Smith over the complex numbers. A key technical ingredient is a new versality argument which allows us to work throughout over a Novikov-type ring with integer coefficients. |
| title | Integrality of mirror maps and arithmetic homological mirror symmetry for Greene--Plesser mirrors |
| topic | Symplectic Geometry Algebraic Geometry Number Theory |
| url | https://arxiv.org/abs/2312.01949 |