Height of \(p\)-adic holomorphic maps in several variables and applications. (Q1396074)

The paper deals with the Nevanlinna theory for \(p\)-adic holomorphic maps from \(\mathbb C^m_p\) into \(\mathbb P^n(\mathbb C_p)\). The \(p\)-adic Nevanlinna theory has been developed by several authors. In particular, Khoai defined the height of \(p\)-adic holomorphic functions of several variables. On the other hand, Cherry-Ye proved a \(p\)-adic analogue of the second Main theorem for the above mentioned maps. In this paper, the author gives a new definition of the height of such a map and proves a \(p\)-adic version of the second Main theorem.