A $p$adic Second Main Theorem
Abstract
Let $\mathbf{K}$ be an algebraically closed field of arbitrary characteristic, complete with respect to a nonarchimedean absolute value $\,$. We establish a Second Main Theorem type estimate for analytic map $f\colon \mathbf{K}\rightarrow\mathbb{P}^n(\mathbf{K})$ 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.
 Publication:

arXiv eprints
 Pub Date:
 May 2024
 DOI:
 10.48550/arXiv.2405.14197
 arXiv:
 arXiv:2405.14197
 Bibcode:
 2024arXiv240514197H
 Keywords:

 Mathematics  Complex Variables;
 Mathematics  Number Theory
 EPrint:
 8 pages, comments are very welcome