The truncated second main theorem of function fields
type: Item
instance of: scholarly article
title: The truncated second main theorem of function fields
zbMATH Open document ID: 0866.11066
published in: Journal of Number Theory
publication date: 1996-07-09T00:00:00Z
review text: This paper proves the function field analogue of Cartan's second main theorem with truncated counting functions in arbitrary characteristic, and the Nochka-Chen theorem (Cartan's conjecture) with truncated counting functions in characteristic zero. In both of these cases, the hyperplanes are required to be defined over the field of constants of the function field. The paper also generalizes the higher-dimensional \(abc\) theorem of Voloch and Brownawell-Masser to characteristic \(p>0\). As a corollary of the Nochka-Chen theorem, the paper extends the result of \textit{M. Ru} and \textit{P.-M. Wong} [Invent. Math. 106, 195-216 (1991; Zbl 0758.14007)] on finiteness of integral points on \(\mathbb{P}^n\) minus \(2n+1\) hyperplanes in general position, to function fields of characteristic zero. Again, the hyperplanes must be defined over the field of constants of the function field. Numerous corollaries are also given, and all results include effective, explicit constants.
Mathematics Subject Classification ID: 11R58
Mathematics Subject Classification ID: 11J25
Mathematics Subject Classification ID: 11J61
Mathematics Subject Classification ID: 11D72
zbMATH DE Number: 883842
zbMATH Keywords: \(abc\) conjecture
zbMATH Keywords: Cartan's conjecture
zbMATH Keywords: Cartan's second main theorem
zbMATH Keywords: truncated counting functions
zbMATH Keywords: function fields
author: Julie Tzu-Yueh Wang
reviewed by: Paul Vojta
MaRDI profile type: Publication
full work available at URL: jnth.1996.0071
OpenAlex ID: W1994279759
DOI: 10.1006/JNTH.1996.0071
description: scientific article; zbMATH DE number 883842