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Tate–Shafarevich groups in anticyclotomic ℤp-extensions at supersingular primes

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  19 February 2009

Mirela Çiperiani
Mirela Çiperiani*
Affiliation:
Mathematics Department, Columbia University, 2990 Broadway, New York, NY 10027, USA (email: [email protected])
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Abstract

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Let E/ℚ be an elliptic curve and p a prime of supersingular reduction for E. Denote by the anticyclotomic ℤp-extension of an imaginary quadratic field K which satisfies the Heegner hypothesis. Assuming that p splits in K/ℚ, we prove that has trivial Λ-corank and, in the process, also show that and both have Λ-corank two.

Keywords

elliptic curvesupersingular reductionSelmer groupTate–Shafarevich group

MSC classification

Secondary: 11G05: Elliptic curves over global fields
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 2 , March 2009 , pp. 293 - 308
Copyright
Copyright © Foundation Compositio Mathematica 2009

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