Selmer Groups and AnticyclotomicZp-extensions

Abstract

AbstractLetE/Qbe an elliptic curve,pa prime andK∞/Kthe anticyclotomicZp-extension of a quadratic imaginary fieldKsatisfying the Heegner hypothesis. In this paper we give a new proof to a theorem of Bertolini which determines the value of the Λ-corank of Selp∞(E/K∞) in the case whereEhas ordinary reduction atp. In the case whereEhas supersingular reduction atpwe make a conjecture about the structure of the module of Heegner points modp. Assuming this conjecture we give a new proof to a theorem of Ciperiani which determines the value of the Λ-corank of Selp∞(E/K∞) in the case whereEhas supersingular reduction atp.