Algebraic Degeneracy of Non-Archimedean Analytic Maps

TL;DR

This paper establishes non-Archimedean analogs of classical results, demonstrating algebraic degeneracy of rigid analytic maps to projective varieties that omit certain divisors, under specific geometric conditions.

Contribution

It introduces new non-Archimedean versions of degeneracy theorems for analytic maps, extending classical complex results to the non-Archimedean setting.

Findings

Proves algebraic degeneracy of non-Archimedean analytic maps under divisor conditions

Extends classical results of Noguchi and Winkelmann to non-Archimedean context

Provides conditions relating divisor components and Neron-Severi group rank

Abstract

We prove non-Archimedean analogs of results of Noguchi and Winkelmann showing algebraic degeneracy of rigid analytic maps to projective varieties omitting an effective divisor with sufficiently many irreducible components relative to the rank of the group they generate in the Neron-Severi group of the variety.