A 𝑝-adic Second Main Theorem

Huynh, Dinh Tuan

doi:10.1090/proc/17125

A $p$-adic Second Main Theorem
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by Dinh Tuan Huynh;

Proc. Amer. Math. Soc. 153 (2025), 1231-1238

DOI: https://doi.org/10.1090/proc/17125

Published electronically: January 21, 2025

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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 $f\colon \mathbf {K}\rightarrow \mathbb {P}^n(\mathbf {K})$ 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.

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