Extension property of semipositive invertible sheaves over a non-archimedean field

TL;DR

This paper proves an extension property for semipositive invertible sheaves on projective schemes over non-archimedean fields and applies it to establish a Nakai-Moishezon criterion for adelic linear series.

Contribution

It introduces an extension property for semipositive sheaves over non-archimedean fields and applies it to develop a Nakai-Moishezon criterion for adelic linear series.

Findings

Extension property for semipositive sheaves established

Nakai-Moishezon criterion for adelic linear series proven

Applications to non-archimedean geometry demonstrated

Abstract

In this article, we prove an extension property of semipositively metrized ample invertible sheaves on a projective scheme over a complete non-archimedean valued field. As an application, we establish a Nakai-Moishezon type criterion for adelically normed graded linear series.