NDLI: Level raising mod 2 and arbitrary 2-Selmer ranks

Content Provider	Scilit
Author	Hung, Bao V. Le Li, Chao
Copyright Year	2016
Description	Journal: Compositio Mathematica 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.
Ending Page	1608
Starting Page	1576
ISSN	00221295
e-ISSN	15705846
DOI	10.1112/s0010437x16007454
Journal	Compositio Mathematica
Issue Number	8
Volume Number	152
Language	English
Publisher	Wiley-Blackwell
Publisher Date	2016-06-01
Access Restriction	Open
Subject Keyword	Journal: Compositio Mathematica Mathematical Physics Selmer Rank Raising Mod
Content Type	Text
Resource Type	Article
Subject	Algebra and Number Theory

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Level raising mod 2 and arbitrary 2-Selmer ranks