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

Levent Alpöge, Manjul Bhargava, Ari Shnidman

Research output: Contribution to journalArticlepeer-review

Abstract

We show that a positive proportion of cubic fields are not monogenic, despite having no local obstruction to being monogenic. Our proof involves the comparison of 2-descent and 3-descent in a certain family of Mordell curves Ek:y2=x3+k. As a by-product of our methods, we show that, for every r≥0, a positive proportion of curves Ek have Tate–Shafarevich group with 3-rank at least r.

Original languageEnglish (US)
JournalMathematische Annalen
DOIs
StateAccepted/In press - 2024

All Science Journal Classification (ASJC) codes

  • General Mathematics

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