Simultaneous supersingular reductions of CM elliptic curves-Reference-Cited by-同舟云学术

Simultaneous supersingular reductions of CM elliptic curves

Published:2022-02-25 Issue:786 Volume:2022 Page:1-43
ISSN:0075-4102
Container-title:Journal für die reine und angewandte Mathematik (Crelles Journal)
language:en
Short-container-title:

Author:

Aka Menny¹,Luethi Manuel²,Michel Philippe²^ORCID,Wieser Andreas³

Affiliation:

1. Departement Mathematik , ETH Zürich , Rämistr. 101, CH-8092 Zurich , Switzerland

2. Institute of Mathematics , Ecole Polytechnique Fédérale de Lausanne , EPFL, Station 8, CH-1015 Lausanne , Switzerland

3. Einstein Institute of Mathematics , Hebrew University , Edward J. Safra Campus , Jerusalem , Israel

Abstract

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.

Publisher

Walter de Gruyter GmbH

Subject

Applied Mathematics,General Mathematics

Link

https://www.degruyter.com/document/doi/10.1515/crelle-2021-0086/pdf

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