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Torsion des variétés abéliennes CM


Authors: Éric Gaudron and Gaël Rémond
Journal: Proc. Amer. Math. Soc. 146 (2018), 2741-2747
MSC (2010): Primary 11G10, 11G15, 14G05, 14K22
DOI: https://doi.org/10.1090/proc/13885
Published electronically: March 30, 2018
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Abstract: In this note, we improve on a result of Silverberg giving an upper bound for the order of a rational torsion point on a CM abelian variety over a number field in terms of the degree of the field and the dimension of the variety. The proof uses the main theorem of complex multiplication and class field theory.


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Additional Information

Éric Gaudron
Affiliation: Université Clermont Auvergne, CNRS, LMBP, F-63000 Clermont-Ferrand, France
Email: Eric.Gaudron@uca.fr

Gaël Rémond
Affiliation: Institut Fourier, UMR 5582, CS 40700, 38058 Grenoble Cedex 9, France
Email: Gael.Remond@univ-grenoble-alpes.fr

DOI: https://doi.org/10.1090/proc/13885
Received by editor(s): April 7, 2017
Received by editor(s) in revised form: June 20, 2017
Published electronically: March 30, 2018
Additional Notes: Le premier auteur remercie la région Auvergne de son aide financière apportée à travers le projet Diophante
Les auteurs ont bénéficié du soutien du projet ANR Gardio 14-CE25-0015.
Communicated by: Romyar T. Sharifi
Article copyright: © Copyright 2018 American Mathematical Society

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