### Tate-Shafarevich groups over anticyclotomic Z p extensions

**Ciperiani, M ***(Columbia)*

Friday 31 July 2009, 11:30-12:30

Seminar Room 1, Newton Institute

#### Abstract

Let E be an elliptic curve over Q with supersingular reduction at p and K an imaginary quadratic extension of Q. We analyze the structure of the p-primary part of the Tate-Shafarevich group of E over the anticyclotomic Z_p-extension K_\infty/K by viewing it as a module over Z_p[Gal(K_\infty/K)].

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