A version of Cartan–Nochka's theorem for non-Archimedean holomorphic curves with integrated reduced counting functions

Abstract

UDC 517.5

Let $\mathbb{K}$ be an algebraically closed field of characteristic $0,$ completed with respect to a non-Archimedean absolute value and let $\mathbb{P}^n(\mathbb{K})$ be an $n$-dimensional projective space over $\mathbb{K}.$ A collection $\mathcal H = \{H_1,\ldots,H_q\} \in \mathbb{P}^n(\mathbb{K}),$ $q \geq N+1,$ is said to be  in $N$-subgeneral position if, for any $1\leq i_1<\ldots<i_{N+1}\leq q,$ we have $\bigcap_{j=1}^{N+1} H_{i_j} = \varnothing.$ We prove a version of the second main theorem for non-Archimedean holomorphic curves intersecting hyperplanes in $N$-subgeneral position with integrated reduced counting functions.