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

Part of: Arithmetic problems. Diophantine geometry Arithmetic algebraic geometry

Published online by Cambridge University Press:  03 December 2009

Jan Nekovář
Jan Nekovář*
Affiliation:
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)
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Abstract

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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.

Keywords

Selmer groupselliptic curvesparity conjecturemodularity

MSC classification

Secondary: 11G40: $L$-functions of varieties over global fields; Birch-Swinnerton-Dyer conjecture 11G05: Elliptic curves over global fields 14G10: Zeta-functions and related questions (Birch-Swinnerton-Dyer conjecture)
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 6 , November 2009 , pp. 1351 - 1359
Copyright
Copyright © Foundation Compositio Mathematica 2009

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