Displaying similar documents to “Heights and reductions of semi-stable varieties”

Local and canonical heights of subvarieties

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...

Perturbations of the metric in Seiberg-Witten equations

Luca Scala (2011)

Annales de l’institut Fourier

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Let M a compact connected oriented 4-manifold. We study the space Ξ of Spin c -structures of fixed fundamental class, as an infinite dimensional principal bundle on the manifold of riemannian metrics on M . In order to study perturbations of the metric in Seiberg-Witten equations, we study the transversality of universal equations, parametrized with all Spin c -structures  Ξ . We prove that, on a complex Kähler surface, for an hermitian metric h sufficiently close to the original Kähler metric, the...

Diophantine approximation on algebraic varieties

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.

Algebraic leaves of algebraic foliations over number fields

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 K embedded in C , a smooth algebraic variety X over K , equipped with a K - rational point P , and F an algebraic subbundle of the its tangent bundle T X , defined over K . Assume moreover that the vector bundle F is involutive, i.e., closed under Lie bracket. Then it defines an holomorphic foliation of the analytic manifold X ( C ) , and one may consider its leaf F through...