2-selmer near-companion curves

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Abstract

Let E and A be elliptic curves over a number field K. Letχ be a quadratic character of K. We prove the conjecture posed by Mazur and Rubin on n-Selmer near-companion curves in the case n = 2. Namely, we show if the difference of the 2-Selmer ranks of Eχ and Aχ is bounded independent of χ, there is a GK -module isomorphism E[2] (Formula Persented) A[2].

Original languageEnglish
Pages (from-to)425-440
Number of pages16
JournalTransactions of the American Mathematical Society
Volume372
Issue number1
DOIs
Publication statusPublished - 2019

Bibliographical note

Publisher Copyright:
© 2018 American Mathematical Society.

All Science Journal Classification (ASJC) codes

  • Mathematics(all)
  • Applied Mathematics

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