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Level raising mod 2 and arbitrary 2-Selmer ranks
Published online by Cambridge University Press: 01 June 2016
Abstract
We prove a level raising mod $\ell =2$ theorem for elliptic curves over
$\mathbb{Q}$. It generalizes theorems of Ribet and Diamond–Taylor and also explains different sign phenomena compared to odd
$\ell$. 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.
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- Research Article
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- © The Authors 2016
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