Level raising mod 2 and arbitrary 2-Selmer ranks

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6 Scopus citations


We prove a level raising mod theorem for elliptic curves over. It generalizes theorems of Ribet and Diamond-Taylor and also explains different sign phenomena compared to odd. We use it to study the 2-Selmer groups of modular abelian varieties with common mod 2 Galois representation. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families.

Original languageEnglish (US)
Pages (from-to)1576-1608
Number of pages33
JournalCompositio Mathematica
Issue number8
StatePublished - Aug 1 2016


  • Selmer groups
  • modular forms

ASJC Scopus subject areas

  • Algebra and Number Theory


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