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

Nekovář, Jan

doi:10.2140/ant.2013.7.1101

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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

DOI: 10.2140/ant.2013.7.1101

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

Vol. 7, No. 5, 2013