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Selmer Groups and Anticyclotomic Zp -extensions

Published online by Cambridge University Press:  12 May 2016

AHMED MATAR
AHMED MATAR*
Affiliation:
Department of Mathematics, University of Bahrain, P.O. Box 32038, Sukhair, Bahrain. e-mail: [email protected]
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Abstract

Let E/Q be an elliptic curve, p a prime and K ∞/K the anticyclotomic Zp -extension of a quadratic imaginary field K satisfying 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 where E has ordinary reduction at p. In the case where E has supersingular reduction at p we make a conjecture about the structure of the module of Heegner points mod p. 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 where E has supersingular reduction at p.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 161 , Issue 3 , November 2016 , pp. 409 - 433
Copyright
Copyright © Cambridge Philosophical Society 2016 

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