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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.17708 |
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| _version_ | 1866908901722554368 |
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| author | Brumer, Armand Kramer, Kenneth |
| author_facet | Brumer, Armand Kramer, Kenneth |
| contents | We extend methods of Fontaine, Abrashkin and Schoof to obtain criteria determining number fields K over which no non-zero abelian variety with everywhere good reduction exists. As an application, under the GRH, we find 24744 such fields of various degrees up to 16. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_17708 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Fields with no everywhere good abelian varieties Brumer, Armand Kramer, Kenneth Number Theory 11G10 (primary), 11S15, 14L15 (secondary) We extend methods of Fontaine, Abrashkin and Schoof to obtain criteria determining number fields K over which no non-zero abelian variety with everywhere good reduction exists. As an application, under the GRH, we find 24744 such fields of various degrees up to 16. |
| title | Fields with no everywhere good abelian varieties |
| topic | Number Theory 11G10 (primary), 11S15, 14L15 (secondary) |
| url | https://arxiv.org/abs/2603.17708 |