Truncated second main theorem for non-Archimedean meromorphic maps

TL;DR

This paper establishes a truncated second main theorem for non-Archimedean meromorphic maps from algebraically closed fields, extending value distribution theory to higher dimensions and subvarieties with hypersurface intersections.

Contribution

It introduces a new second main theorem for non-Archimedean meromorphic maps intersecting hypersurfaces in subgeneral position, with truncated counting functions.

Findings

Proves a truncated second main theorem in the non-Archimedean setting.

Extends classical value distribution results to higher-dimensional non-Archimedean maps.

Addresses intersections with hypersurfaces in subgeneral position.

Abstract

Let $\mathbb F$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of $\mathbb P^M(\mathbb F)$. In this paper, we will prove some second main theorems for non-Archimedean meromorphic maps of $\mathbb F^m$ into $V$ intersecting a family of hypersurfaces in $N-$subgeneral position with truncated counting functions.