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Abstract

In this paper, several second main theorems are given for the non-Archimedean meromorphic map $f:{\mathbb {F}}^m\rightarrow {\mathbb {P}}^n$ intersecting hyperplanes in ${\mathbb {P}}^n$ in terms of the truncated counting functions defined by W. Cherry and C. Toropu, where ${\mathbb {F}}$ is an algebraically closed field of characteristic $p\ge 0$ complete with respect to a non-Archimedean absolute value. As an application, the uniqueness problem for non-Archimedean meromorphic maps sharing hyperplanes is also discussed.