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Sur la hauteur de Faltings des variétés abéliennes à multiplication complexe

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Compositio Mathematica

Abstract

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.

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Références

  1. Bost, J.B.: Arakelov geometry of abelian varieties, dans ‘Conference on Arithmetical Geometry’, Berlin, March 21-26, 1996, Max-Planck Institut für Mathematik Bonn, preprint 96-51.

  2. Bost, J.-B.: Périodes et isogénies des variétés abéliennes sur les corps de nombres (d’après D. Masser et G. Wüstholz), exposé Bourbaki 795, Astérisque237 (1996) 115-161.

    Google Scholar 

  3. Colmez, P.: Périodes des variétés abéliennes à multiplication complexe, Ann. of Math. 138 (1993) 625-683.

    Google Scholar 

  4. Davenport, H.: Multiplicative Number Theory, Markham, Chicago, 1967.

  5. Dixmier, J.: Les C*-Algèbres et Leurs Représentations, Gauthiers-Villars,Paris, 1964.

    Google Scholar 

  6. Ellison, J., Mendès, FranceM.: LesNombres Premiers, Publications de l’université de Nancago IX, Hermann, Paris, 1975.

    Google Scholar 

  7. Masser, D., Wüstholz, G.: Endomorphism estimates for abelian varieties, Math. Zeit. 215 (1994) 641-653.

    Google Scholar 

  8. Nakkajima, Y., Taguchi, Y.: A generalization of the Chowla-Selberg formula, J. reine angew. Math.419 (1991) 119-124.

    Google Scholar 

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Authors and Affiliations

  1. Département de Mathématiques et informatique École Normale supérieur, U.R.A. 1327 du C.N.R.S., 45 rue d'ULM, 75005, Paris, France

    Pierre Colmez

  2. 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

    Pierre Colmez

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  1. Pierre Colmez
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Colmez, P. Sur la hauteur de Faltings des variétés abéliennes à multiplication complexe. Compositio Mathematica 111, 359–369 (1998). https://doi.org/10.1023/A:1000390105495

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  • DOI: https://doi.org/10.1023/A:1000390105495

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