Arithmetic Fujita approximation

TL;DR

This paper establishes an arithmetic analogue of Fujita's approximation theorem within Arakelov geometry, confirming a conjecture by Moriwaki through advanced slope methods and measure theory related to real filtrations.

Contribution

It introduces an arithmetic version of Fujita's approximation theorem, expanding the theoretical framework in Arakelov geometry and confirming Moriwaki's conjecture.

Findings

Proves an arithmetic analogue of Fujita's approximation theorem

Uses slope method and measures from $\\mathbb R$-filtrations

Confirms Moriwaki's conjecture

Abstract

We prove an arithmetic analogue of Fujita's approximation theorem in Arakelov geometry, conjectured by Moriwaki, by using slope method and measures associated to $\mathbb R$-filtrations.