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Mathematics > Number Theory
Title: Simultaneous supersingular reductions of CM elliptic curves
(Submitted on 4 May 2020 (v1), last revised 24 Nov 2021 (this version, v2))
Abstract: We study the simultaneous reductions at several supersingular primes of elliptic curves with complex multiplication. We show -- under additional congruence assumptions on the CM order -- that the reductions are surjective (and even become equidistributed) on the product of supersingular loci when the discriminant of the order becomes large. This variant of the equidistribution theorems of Duke and Cornut-Vatsal is an(other) application of the recent work of Einsiedler and Lindenstrauss on the classification of joinings of higher-rank diagonalizable actions.
Submission history
From: Philippe Michel G [view email][v1] Mon, 4 May 2020 14:49:10 GMT (596kb)
[v2] Wed, 24 Nov 2021 18:40:42 GMT (51kb)
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