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Journals and Conferences
— 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 study the semistability of the tensor product of hermitian vector bundles by using the ε-tensor product and the geometric (semi)stability of vector subspaces in the tensor product of two vector spaces. Notably, for any number field K and any hermitian vector bundles E and F over SpecOK , we show that the maximal slopes of E, F , and E ⊗ F satisfy the… (More)
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 show an arithmetic generalization of the recent work of Lazarsfeld–Mustaţǎ which uses Okounkov bodies to study linear series of line bundles. As applications, we derive a log-concavity inequality on volumes of arithmetic line bundles and an arithmetic Fujita approximation theorem for big line bundles.
— 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)
— 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 establish an explicit link between the volume function on a projective 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.