Submodules of products of quasi-periodic modules
type: Item
instance of: scholarly article
title: Submodules of products of quasi-periodic modules
zbMATH Open document ID: 0881.11056
author: W. Dale Brownawell
published in: Rocky Mountain Journal of Mathematics
publication date: 1997-11-16T00:00:00Z
full work available at URL: contents.htm
review text: Following the work of \textit{E. M. Kolchin} [Am. J. Math. 90, 1151-1164 (1968; Zbl 0169.36701)], algebraic subgroups of products of simple algebraic groups have been studied by \textit{W. D. Brownawell} and \textit{K. K. Kubota} [Acta Arith. 33, No. 2, 111-149 (1977; Zbl 0356.10027)], in order to deduce results of algebraic independence of certain periodic or quasi-periodic complex functions, and of their values. Here, the authors perform a similar investigation for Drinfeld modules. The conclusion of the analytic subgroup theorem of \textit{Jing Yu} [Ann. Math., II. Ser. 145, 215-233 (1997; Zbl 0881.11056)] involves \(t\)-submodules of a given \(t\)-module \(G\), and it is therefore of the utmost importance to have a description of these. This is the goal of the present paper for the case where \(G\) is a product of various Drinfeld modules and quasi periodic modules (associated with biderivations). Among the main results of the present paper is a characterization of algebraic submodules of products of quasi periodic modules.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 11J99
zbMATH DE Number: 1026392
zbMATH Keywords: Drinfeld modules
zbMATH Keywords: Carlitz module
zbMATH Keywords: \(t\)-submodules
zbMATH Keywords: Kolchin's theorem
zbMATH Keywords: quasi-periodic modules
zbMATH Keywords: biderivations
reviewed by: Michel Waldschmidt
MaRDI profile type: Publication
OpenAlex ID: W1992165575
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DOI: 10.1216/RMJM/1181072026
description: scientific article; zbMATH DE number 1026392