Faltings heights of abelian varieties with complex multiplication

被引：25

作者：

Colmez, P

机构：

[1] Ecole Normale Super, CNRS, Dept Math & Informat, URA 1327, F-75005 Paris, France

[2] CNRS, Equipe Arithmet, Inst Math, UMR 9994, F-75252 Paris 05, France

来源：

COMPOSITIO MATHEMATICA | 1998年 / 111卷 / 03期

关键词：

complex multiplication; Faltings' height; Siegel's zeroes; Artin L-functions;

D O I：

10.1023/A:1000390105495

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

Motivated by a result of Bost, we use the relationship between Faltings' heights of abelian varieties with complex multiplication and logarithmic derivatives of Artin L-functions at s = 0 to investigate these heights. In particular, we prove that the height of an elliptic curve with complex multiplication by Q(root-d) is bounded from below by an effective affine function of log d.

引用

页码：359 / 368

页数：10

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