Submodules of products of quasi-periodic modules
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.
scientific article; zbMATH DE number 1026392
scientific article