TY - JOUR
T1 - A positive proportion of quartic fields are not monogenic yet have no local obstruction to being so
AU - Alpöge, Levent
AU - Bhargava, Manjul
AU - Shnidman, Ari
N1 - Publisher Copyright:
© The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature 2023.
PY - 2024/4
Y1 - 2024/4
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=85156097930&partnerID=8YFLogxK
U2 - 10.1007/s00208-023-02575-0
DO - 10.1007/s00208-023-02575-0
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AN - SCOPUS:85156097930
SN - 0025-5831
VL - 388
SP - 4037
EP - 4052
JO - Mathematische Annalen
JF - Mathematische Annalen
IS - 4
ER -