|Joint IAS/Princeton University Number Theory Seminar|
|Topic:||Level raising mod 2 and arbitrary 2-Selmer ranks|
|Date:||Thursday, December 4|
|Time/Room:||4:30pm - 5:30pm/S-101|
We prove a level raising mod $p = 2$ theorem for elliptic curves over $\mathbb Q$, 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.