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.
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页码：359 / 368
页数：10
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