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Sur la hauteur de Faltings des variétés abéliennes à multiplication complexe

Published online by Cambridge University Press:  04 December 2007

PIERRE COLMEZ
PIERRE COLMEZ
Affiliation:
Département de Mathématiques et informatique École Normale supérieur, U.R.A. 1327 du C.N.R.S., 45 rue d‘ULM, 75005 Paris, France; e-mail: colmez@dmi.ens.fr Équipe d‘arithmétique, Institut de mathématiques, U.M.R. 9994 du C.N.R.S., Tour 46-56 -5ème étage4- Boite 247, 4 place Jussieu, 75252 Paris Cedex 05, France
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Abstract

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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 $Q√-d$ is bounded from below by an effective affine function of log d.

Keywords

Complex multiplicationFaltings‘ heightSiegel‘s zeroesArtin L-functions.
Type
Research Article
Information
Compositio Mathematica , Volume 111 , Issue 3 , May 1998 , pp. 359 - 369
Copyright
© 1998 Kluwer Academic Publishers