Free basis consisting of strictly small sections

TL;DR

This paper establishes conditions under which a free basis of strictly small sections can be constructed on an arithmetic variety, contributing to the understanding of arithmetic geometry and the structure of sections.

Contribution

It introduces new mild conditions that ensure the existence of a free basis of strictly small sections on arithmetic varieties.

Findings

Identifies sufficient conditions for free bases of strictly small sections.

Provides a framework for constructing such bases under these conditions.

Enhances understanding of the structure of sections in arithmetic geometry.

Abstract

In this paper, we consider mild and appropriate conditions to guarantee a free basis consisting of strictly small sections on an arithmetic variety.