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We propose a generalization of Quillen's exact category — arithmetic exact category and we discuss conditions on such categories under which one can establish the notion of Harder-Narasimhan filtrations and Harder-Narsimhan polygons. Furthermore, we show the functoriality of Harder-Narasimhan filtrations (indexed by R), which can not be stated in the(More)
— We prove an arithmetic analogue of Fujita's approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using slope method and measures associated to R-filtrations. Résumé. — On démontre un analogue arithmétique du théorème d'approximation de Fujita en géométrie d'Arakelov — conjecturé par Moriwaki — par la méthode de pentes et les mesures(More)
— We introduce the positive intersection product in Arakelov geometry and prove that the arithmetic volume function is continuously differentiable. As applications, we compute the distribution function of the asymptotic measure of a Hermitian line bundle and several other arithmetic invariants. Résumé. — On introduit le produit d'intersection positive en(More)
— Let L be a big invertible sheaf on a complex projective variety, equipped with two continuous metrics. We prove that the distribution of the eigen-values of the transition matrix between the L 2 norms on H 0 (X, nL) with respect to the two metriques converges (in law) as n goes to infinity to a Borel probability measure on R. This result can be thought of(More)