Small height in fields generated by singular moduli

Galateau, Aurélien

doi:10.1090/proc/13058

Small height in fields generated by singular moduli
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Proc. Amer. Math. Soc. 144 (2016), 2771-2786 Request permission

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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