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Small height in fields generated by singular moduli


Author: Aurélien Galateau
Journal: Proc. Amer. Math. Soc. 144 (2016), 2771-2786
MSC (2010): Primary 11G50; Secondary 11G05, 14H52, 14G40
DOI: https://doi.org/10.1090/proc/13058
Published electronically: March 18, 2016
MathSciNet review: 3487213
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Abstract: We prove that some fields generated by $ j$-invariants of CM elliptic curves (of infinite dimension over $ \mathbb{Q}$) satisfy the Property (B). The singular moduli are chosen so as to have supersingular reduction simultaneously above a fixed prime $ q$, which provides strong $ q$-adic estimates leading to an explicit lower bound for the height.


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Aurélien Galateau
Affiliation: Laboratoire de Mathémathiques de Besançon, Université de Franche-Comté, CNRS, 16 route de Gray, 25030 Besnançon, France
Email: aurelien.galateau@univ-fcomte.fr

DOI: https://doi.org/10.1090/proc/13058
Received by editor(s): June 20, 2015
Published electronically: March 18, 2016
Communicated by: Ken Ono
Article copyright: © Copyright 2016 American Mathematical Society