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| HAL : hal-00133406, version 1 |
| arXiv : math.NT/0702593 |
| Fiche détaillée |  Récupérer au format |
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| Algebra, arithmetic, and geometry: in honor of Yu. I. Manin. Vol. I, Yuri Tschinkel and Yuri Zarhin (Ed.) (2009) 69-124 |
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| Analytic curves in algebraic varieties over number fields |
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| Jean-Benoît Bost 1Antoine Chambert-Loir 2 |
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| (2009) |
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| We establish algebraicity criteria for formal germs of curves in algebraic varieties over number fields and apply them to derive a rationality criterion for formal germs of functions, which extends the classical rationality theorems of Borel-Dwork and Pólya-Bertrandias valid over the projective line to arbitrary algebraic curves over a number field. The formulation and the proof of these criteria involve some basic notions in Arakelov geometry, combined with complex and rigid analytic geometry (notably, potential theory over complex and p-adic curves). We also discuss geometric analogues, pertaining to the algebraic geometry of projective surfaces, of these arithmetic criteria. |
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| 1 : | Laboratoire de Mathématiques d'Orsay (LM-Orsay) |
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CNRS : UMR8628 – Université Paris XI - Paris Sud |
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| 2 : | Institut de Recherche Mathématique de Rennes (IRMAR) |
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CNRS : UMR6625 – Université de Rennes 1 – École normale supérieure de Cachan - ENS Cachan – Institut National des Sciences Appliquées (INSA) : - RENNES – Université de Rennes II - Haute Bretagne |
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| Domaine | : | Mathématiques/Théorie des nombres Mathématiques/Géométrie algébrique |
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| Lien vers le texte intégral : |
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| http://fr.arXiv.org/abs/math.NT/0702593 |
| hal-00133406, version 1 | |
| http://hal.archives-ouvertes.fr/hal-00133406 | |
| oai:hal.archives-ouvertes.fr:hal-00133406 | |
| Contributeur : Antoine Chambert-Loir | |
| Soumis le : Lundi 26 Février 2007, 11:38:44 | |
| Dernière modification le : Mardi 19 Juillet 2011, 14:46:02 | |
