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Title of Journal: manuscripta math

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Abbravation: Manuscripta Mathematica

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Springer Berlin Heidelberg

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DOI

10.1016/0958-2118(93)90228-E

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1432-1785

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Minoration de la hauteur de NéronTate sur les sur

Authors: Fabien Pazuki
Publish Date: 2012/10/26
Volume: 142, Issue: 1-2, Pages: 61-99
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Abstract

This paper contains results concerning a conjecture made by Lang and Silverman predicting a lower bound for the canonical height on abelian varieties of dimension 2 over number fields The method used here is a local height decomposition We derive as corollaries uniform bounds on the number of torsion points on families of abelian surfaces and on the number of rational points on families of genus 2 curvesOn obtient dans le présent texte des résultats en direction d’une conjecture de Lang et Silverman de minoration de la hauteur canonique sur les variétés abéliennes de dimension 2 sur un corps de nombres La méthode utilisée est une décomposition en hauteurs locales On déduit en corollaire une borne uniforme sur la torsion de familles de surfaces abéliennes et une borne uniforme sur le nombre de points rationnels de familles de courbes de genre 2

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Other Papers In This Journal:
  1. A stability criterion for nonparametric minimal submanifolds
  2. Harmonic maps and asymptotic Teichmüller space
  3. On the backward uniqueness property for the heat equation in two-dimensional conical domains
  4. Stability of flows associated to gradient vector fields and convergence of iterated transport maps
  5. Willmore submanifolds of the Möbius space and a Bernstein-type theorem
  6. A positivity property of the Satake isomorphism
  7. Homological characterization of lean algebras
  8. Reduction of structure for torsors over semilocal rings
  9. Common divisors of elliptic divisibility sequences over function fields
  10. Finitistic dimensions of semiprimary rings
  11. Extending Elliptic Curve Chabauty to higher genus curves
  12. The Sp 3 -grassmannian and duality for prime Fano threefolds of genus 9
  13. Existence and compactness for the $${\overline{\partial}}$$ -Neumann operator on q-convex domains
  14. The normalization constant of a certain invariant measure on GL n ()
  15. Tropical descendant Gromov–Witten invariants
  16. A Harnack inequality for the quasi-minima of scalar integral functionals with general growth conditions
  17. Cut loci and conjugate loci on Liouville surfaces
  18. A sphere theorem on locally conformally flat even-dimensional manifolds
  19. On the class numbers of certain Hilbert class fields
  20. The zeros of certain weakly holomorphic Drinfeld modular forms
  21. Icosahedral representations and elliptic curves
  22. On entire functions whose derivatives are¶integer-valued on geometric progressions
  23. Perversité et variation
  24. On linear combinations of special values of L -functions
  25. Irrationalité de certaines sommes de séries
  26. Deformations of Koszul Artin–Schelter Gorenstein algebras
  27. On positive definite hermitian forms
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