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arXiv · 1501.01344

Level raising mod 2 and arbitrary 2-Selmer ranks

Bao V. Le Hung·Chao Li
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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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Bao V. Le Hung, Chao Li. 2015-01-07. Level raising mod 2 and arbitrary 2-Selmer ranks. https://arxiv.org/abs/1501.01344

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