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

共 50 条

[1] Faltings heights of abelian varieties with complex multiplication
Andreatta, Fabrizio
Goren, Eyal Z.
Howard, Benjamin
Pera, Keerthi Madapusi
ANNALS OF MATHEMATICS, 2018, 187 (02) : 391 - 531
[2] Smallness of Faltings heights of CM abelian varieties
Wei, Xunjing
JOURNAL OF NUMBER THEORY, 2023, 242 : 73 - 101
[3] ABELIAN VARIETIES WITH COMPLEX MULTIPLICATION
SHIMURA, G
PROCEEDINGS OF THE LONDON MATHEMATICAL SOCIETY, 1977, 34 (JAN) : 65 - 86
[4] On the abelian varieties with complex multiplication.
Humbert, G.
COMPTES RENDUS HEBDOMADAIRES DES SEANCES DE L ACADEMIE DES SCIENCES, 1902, 134 : 1261 - 1266
[5] ARITHMETIC ABELIAN-VARIETIES WITH COMPLEX MULTIPLICATION
SCHMIDT, CG
LECTURE NOTES IN MATHEMATICS, 1984, 1082 : R7 - 96
[6] Tate Cycles on Abelian Varieties with Complex Multiplication
Murty, V. Kumar
Patankar, Vijay M.
CANADIAN JOURNAL OF MATHEMATICS-JOURNAL CANADIEN DE MATHEMATIQUES, 2015, 67 (01): : 198 - 213
[7] DIOPHANTINE APPROXIMATION ON ABELIAN VARIETIES WITH COMPLEX MULTIPLICATION
LANG, S
ADVANCES IN MATHEMATICS, 1975, 17 (03) : 281 - 336
[8] PERIODS OF ABELIAN-VARIETIES WITH COMPLEX MULTIPLICATION
COLMEZ, P
ANNALS OF MATHEMATICS, 1993, 138 (03) : 625 - 683
[9] EXISTENCE OF SIMPLE ABELIAN VARIETIES WITH COMPLEX MULTIPLICATION
SCHAPPACHER, N
JOURNAL FUR DIE REINE UND ANGEWANDTE MATHEMATIK, 1977, 292 : 186 - 190
[10] Selmer groups of certain abelian varieties with complex multiplication
Li, Yong-Xiong
ACTA ARITHMETICA, 2022, 203 (04) : 289 - 305

← 1 2 3 4 5 →