Fields with no everywhere good abelian varieties
Number Theory
2026-03-23 v2
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.
Keywords
Cite
@article{arxiv.2603.17708,
title = {Fields with no everywhere good abelian varieties},
author = {Armand Brumer and Kenneth Kramer},
journal= {arXiv preprint arXiv:2603.17708},
year = {2026}
}
Comments
Corrected link to data files