Simultaneous supersingular reductions of CM elliptic curves

被引：5

作者：

Aka, Menny ^{[1
]}

Luethi, Manuel ^{[2
]}

Michel, Philippe ^{[2
]}

Wieser, Andreas ^{[3
]}

机构：

[1] Swiss Fed Inst Technol, Dept Math, Ramistr 101, CH-8092 Zurich, Switzerland

[2] Ecole Polytech Fed Lausanne, Inst Math, Stn 8, CH-1015 Lausanne, Switzerland

[3] Hebrew Univ Jerusalem, Einstein Inst Math, Edward J Safra Campus, Jerusalem, Israel

来源：

JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK | 2022年 / 2022卷 / 786期

关键词：

SUBCONVEXITY PROBLEM; INTEGER POINTS; EQUIDISTRIBUTION; LIFTINGS; SPHERES; VALUES;

D O I：

10.1515/crelle-2021-0086

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

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.

引用

页码：1 / 43

页数：43

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