Compositio Mathematica

Table of Contents - 2008 - Volume 144, Issue 04  

Research Article

Global divisibility of Heegner points and Tamagawa numbers

Dimitar Jetcheva1

a1 Department of Mathematics, University of California at Berkeley, Berkeley, CA 94720, USA (email: jetchev@math.berkeley.edu)

Abstract

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.

(Received September 18 2007)

(Accepted January 09 2008)

2000 Mathematics subject classification

  • 11G05

Keywords

  • elliptic curves;
  • Heegner points;
  • Selmer groups;
  • Birch and Swinnerton-Dyer conjecture

Footnotes

In memory of my father and my grandfather