Fields with no everywhere good abelian varieties

Armand Brumer; Kenneth Kramer

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arXiv · 2603.17708

Fields with no everywhere good abelian varieties

Armand Brumer·Kenneth Kramer

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Abstract

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.

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Armand Brumer, Kenneth Kramer. 2026-03-18. Fields with no everywhere good abelian varieties. https://arxiv.org/abs/2603.17708

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