Vol. 7, No. 5, 2013

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Some consequences of a formula of Mazur and Rubin for arithmetic local constants

Jan Nekovář

Vol. 7 (2013), No. 5, 1101–1120
Abstract

We prove a very general case of the parity conjecture for Selmer groups of elliptic curves over totally real fields, as well as slightly less general results for classical modular forms, Hilbert modular forms of parallel weight two and for abelian varieties with real multiplication.

Keywords
Selmer groups, parity, elliptic curves, modular forms
Mathematical Subject Classification 2010
Primary: 11G40
Milestones
Received: 3 October 2011
Revised: 18 May 2012
Accepted: 18 May 2012
Published: 6 September 2013
Authors
Jan Nekovář
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