The Truncated Second Main Theorem of Function Fields

Abstract

We formulate some results of function fields which are analogous to Cartan's Second Main Theorem with truncated counting functions, Cartan's conjecture, and the generalized Picard Theorem. We also give a generalization of function fields version ofabc-conjecture due to Mason, Voloch, Brownawell, and Masser. A result of the finiteness of theS-integral points of function fields of characteristic 0 in the complement of 2n+1 hyperplanes with constant coefficients and in general position is obtained in this paper.