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arXiv · 2107.05514

A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so

Levent Alpöge·Manjul Bhargava·Ari Shnidman
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Abstract

We show that a positive proportion of quartic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof builds on the corresponding result for cubic fields that we obtained in a previous work. Along the way, we also prove that a positive proportion of quartic rings of integers do not arise as the invariant order of an integral binary quartic form despite having no local obstruction.

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Levent Alpöge, Manjul Bhargava, Ari Shnidman. 2021-07-12. A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so. https://arxiv.org/abs/2107.05514

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