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Global divisibility of Heegner points and Tamagawa numbers

Part of: Arithmetic algebraic geometry

Published online by Cambridge University Press:  01 July 2008

Dimitar Jetchev
Dimitar Jetchev*
Affiliation:
Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA (email: jetchev@math.berkeley.edu)
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Abstract

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We improve Kolyvagin’s upper bound on the order of the p-primary part of the Shafarevich–Tate group of an elliptic curve of rank one over a quadratic imaginary field. In many cases, our bound is precisely that predicted by the Birch and Swinnerton-Dyer conjectural formula.

Keywords

elliptic curvesHeegner pointsSelmer groupsBirch and Swinnerton-Dyer conjecture

MSC classification

Secondary: 11G05: Elliptic curves over global fields
Type
Research Article
Information
Compositio Mathematica , Volume 144 , Issue 4 , July 2008 , pp. 811 - 826
Copyright
Copyright © Foundation Compositio Mathematica 2008