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Arithmetic Fujita approximation

Huayi Chen — 2010

Annales scientifiques de l'École Normale Supérieure

We prove an arithmetic analogue of Fujita’s approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using measures associated to -filtrations.

Fonction de Seshadri arithmétique en géométrie d’Arakelov

Huayi Chen — 2014

Annales de la faculté des sciences de Toulouse Mathématiques

To any adelic invertible sheaf on a projective arithmetic variety and any regular algebraic point of the arithmetic variety, we associate a function defined on which measures the separation of jets on this algebraic point by the “small” sections of the adelic invertible sheaf. This function will be used to study the arithmetic local positivity.

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