Level raising mod 2 and arbitrary 2-Selmer ranks

Bao V. Le Hung; Chao Li

doi:10.1112/S0010437X16007454

Level raising mod 2 and arbitrary 2-Selmer ranks

Bao V. Le Hung, Chao Li

Mathematics

Research output: Contribution to journal › Article › peer-review

6 Scopus citations

Abstract

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 modÂ 2 Galois representation. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families.

Original language	English (US)
Pages (from-to)	1576-1608
Number of pages	33
Journal	Compositio Mathematica
Volume	152
Issue number	8
DOIs	https://doi.org/10.1112/S0010437X16007454
State	Published - Aug 1 2016

Keywords

Selmer groups
modular forms

ASJC Scopus subject areas

Algebra and Number Theory

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10.1112/S0010437X16007454

Cite this

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abstract = "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{\^A} 2 Galois representation. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families.",

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KW - modular forms

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Level raising mod 2 and arbitrary 2-Selmer ranks

Abstract

Keywords

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