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 language | American English |
---|---|
Journal | Mathematische Annalen |
DOIs | |
State | Accepted/In press - 2023 |
Bibliographical note
Funding Information:The authors thank Dan Fess and Arul Shankar for many helpful conversations. The first author was supported by NSF Grant DMS-2002109. The second author was supported by a Simons Investigator Grant and NSF Grant DMS-1001828. The third author was supported by the Israel Science Foundation (Grant No. 2301/20).
Publisher Copyright:
© 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.