Successive minima on arithmetic varieties
C. Soulé (1995)
Compositio Mathematica
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C. Soulé (1995)
Compositio Mathematica
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Walter Gubler (2003)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Classical results of Weil, Néron and Tate are generalized to local heights of subvarieties with respect to hermitian pseudo-divisors. The local heights are well-defined if the intersection of supports is empty. In the archimedean case, the metrics are hermitian and the local heights are defined by a refined version of the -product of Gillet-Soulé developped on compact varieties without assuming regularity. In the non-archimedean case, the local heights are intersection numbers using...
Edoardo Vesentini (1966)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Luca Scala (2011)
Annales de l’institut Fourier
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Let a compact connected oriented 4-manifold. We study the space of -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all -structures . We prove that, on a complex Kähler surface, for an hermitian metric sufficiently close to the original Kähler metric, the...
Michael Nakamaye (1999)
Journal de théorie des nombres de Bordeaux
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We present an overview of recent advances in diophantine approximation. Beginning with Roth's theorem, we discuss the Mordell conjecture and then pass on to recent higher dimensional results due to Faltings-Wustholz and to Faltings respectively.
Jean-Michel Bismut (1990)
Bulletin de la Société Mathématique de France
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Jean-Benoît Bost (2001)
Publications Mathématiques de l'IHÉS
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We prove an algebraicity criterion for leaves of algebraic foliations defined over number fields. Namely, consider a number field embedded in , a smooth algebraic variety over , equipped with a rational point , and an algebraic subbundle of the its tangent bundle , defined over . Assume moreover that the vector bundle is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold , and one may consider its leaf through...