# Level raising mod 2 and arbitrary 2-Selmer ranks

## Chao Li (Harvard)

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.

Tuesday, March 31st, at 4:00pm in HBH 227

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