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Approximation de Quasi-Périodes de Variétés Abéliennes by Grinspan-P

Approximation de Quasi-Périodes de Variétés Abéliennes

by Grinspan-P
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Book cover type: Paperback
  • ISBN13: 9786131512971
  • Binding: Paperback
  • Subject: N/A
  • Publisher: Omniscriptum
  • Publisher Imprint: Omniscriptum
  • Publication Date:
  • Pages: 108
  • Original Price: GBP 33.0
  • Language: French
  • Edition: N/A
  • Item Weight: 168 grams
  • BISAC Subject(s): Algebra / General

Périodes et "quasi-périodes" d''une variété abélienne A définie sur un sous-corps de C s''obtiennent par intégration, le long des chemins fermés sur A(C), des différentielles rationnelles sur A, méromorphes et sans résidus de sorte que ces intégrales soient bien définies. Au premier chapitre de la thèse, la méthode modulaire de Barré, Diaz, Gramain, Philibert et Nesterenko est utilisée pour obtenir notamment une mesure d''approximation algébrique du quotient d''une période d''une courbe elliptique définie sur Q par sa quasi-période associée, améliorant un résultat récent de N. Saradha. Puis, dans la deuxième partie, nous étudions diverses extensions possibles des théorèmes de Chudnovsky (des années 70) sur l''indépendance algébrique de quasi-périodes de courbes elliptiques - extensions aux variétés abéliennes de dimension quelconque, et résultats d''approximation (algébrique) simultanée précisant les assertions d''indépendance algébrique. Au coeur des deux parties se trouve une astuce suggérée par Chudnovsky au début des années 80, consistant à faire apparaître des propriétés de G-fonctions dans les estimations arithmétiques de la preuve de transcendance.

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