@article{d4edd62ffd804707ad051c4cb778f4e2,
title = "A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so",
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.",
author = "Levent Alp{\"o}ge and Manjul Bhargava and Ari Shnidman",
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: {\textcopyright} 2023, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.",
year = "2023",
doi = "10.1007/s00208-023-02575-0",
language = "English (US)",
journal = "Mathematische Annalen",
issn = "0025-5831",
publisher = "Springer New York",
}