NAG

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)].