A $p$-adic Second Main Theorem

Abstract

Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a non-archimedean absolute value $||$. We establish a Second Main Theorem type estimate for analytic map $f:\mathbf{K}\to {\mathbb{P}}^n(\mathbf{K})$ and a family of $n$ hypersurfaces in ${\mathbb{P}}^n(\mathbf{K})$ intersecting transversally and not all being hyperplanes. This implements the previous work of Levin where the case of all hypersurfaces having degree greater than one was studied.

arXiv comment8 pages, comments are very welcome