Truncated second main theorem for non-Archimedean meromorphic maps

Let $\mathbb{F}$ be an algebraically closed field of characteristic $p\ge 0$, which is complete with respect to a non-Archimedean absolute value. Let $V$ be a projective subvariety of ${\mathbb{P}}^M(\mathbb{F})$. In this paper, we will prove some second main theorems for non-Archimedean meromorphic maps of ${\mathbb{F}}^m$ into $V$ intersecting a family of hypersurfaces in $N-$subgeneral position with truncated counting functions.