Regulators of Elliptic Curves

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We study the regulator of the Mordell–Weil group of elliptic curves over number fields, functions fields of characteristic 0 or function fields of characteristic p>0⁠. We prove a new Northcott property for the regulator of elliptic curves of rank at least 4 defined over a number field. In the function field case, we obtain that non-trivial families of elliptic curves with bounded regulators and bounded ranks are limited families. We conclude by asking new questions.
Original languageEnglish
JournalInternational Mathematics Research Notices
Volume2021
Issue number7
Pages (from-to)4976–4993
ISSN1073-7928
DOIs
Publication statusPublished - 2021

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