Level raising mod 2 and arbitrary 2-Selmer ranks

Level raising mod 2 and arbitrary 2-Selmer ranks

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Chao Li , Harvard University
IAS Room S-101

We prove a level raising mod p=2 theorem for elliptic curves over Q, generalizing theorems of Ribet and Diamond-Taylor. As an application, we show that the 2-Selmer rank can be arbitrary in level raising families. We will begin by explaining our motivation from W. Zhang's approach to the p-part of the BSD conjecture. Explicit examples will be given to illustrate different phenomena compared to odd p. This is joint work with Bao V. Le Hung.