Compositio Mathematica

Research Article

On the parity of ranks of Selmer groups IV. With an appendix by Jean-Pierre Wintenberger

Jan Nekovářa1

a1 Institut de Mathématiques de Jussieu, Université Pierre et Marie Curie (Paris 6), Théorie des Nombres (Case 247), 4, place Jussieu, F-75252 Paris cedex 05, France (email: nekovar@math.jussieu.fr)

Abstract

We prove the parity conjecture for the ranks of p-power Selmer groups (p⁄=2) of a large class of elliptic curves defined over totally real number fields.

(Received January 07 2008)

(Accepted October 24 2008)

2000 Mathematics Subject Classification

  • 11G40 (primary);
  • 11G05;
  • 14G10 (secondary)

Keywords

  • Selmer groups;
  • elliptic curves;
  • parity conjecture;
  • modularity