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

Levent Alpöge, Manjul Bhargava, Ari Shnidman*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

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.

Original languageAmerican English
Pages (from-to)4037-4052
Number of pages16
JournalMathematische Annalen
Volume388
Issue number4
DOIs
StatePublished - Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.

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