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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)
— By using the slope method, we obtain an explicit uniform estimation for the density of rational points in an arithmetic projective variety with given degree and dimension, embedded in a given arithmetic projective space. Résumé. — On obtient, en utilisant la méthode de pentes, une estimation uniforme et explicite de la densité des points rationnels dans… (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)
We establish in this article convergence results of normalized Harder-Narasimhan polygons both in geometric and in arithmetic frameworks by introducing the Harder-Narasimhan filtration indexed by R and the associated Borel probability measure.
— 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)
— We establish an explicit link between the volume function on a projec-tive variety fibered on a curve and the asymptotic behaviour of the canonical filtration of direct images. As an application, we calculate explicitly the volume function on projective bundle over a curve.