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Tate-Shafarevich groups over anticyclotomic Z p extensions

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Non-Abelian Fundamental Groups in Arithmetic Geometry

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)].

This talk is part of the Isaac Newton Institute Seminar Series series.

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