Generalized theta functions, Drinfeld modules and some arithmetic consequences
type: Item
instance of: scholarly article
title: Generalized theta functions, Drinfeld modules and some arithmetic consequences
zbMATH Open document ID: 1064.11042
published in: Journal of Number Theory
publication date: 2005-04-07T00:00:00Z
review text: Let \(C\) be a smooth, proper and geometrically irreducible curve defined over a finite field \(\mathbb{F}_q\). In the paper under review, the author determines Plücker coordinates for rank-\(n\) Drinfeld modules. The coordinates are obtained by means of the values that certain theta functions take over the module, these theta functions being defined as sections of the generalized theta divisor (as defined by \textit{J.-M. Drezet} and \textit{M. S. Narasimhan} [Invent. Math. 97, No. 1, 53--94 (1989; Zbl 0689.14012)]) on the moduli space of vector bundles over \(C\). After determining the coordinates the author proceeds to use some of the results obtained to establish an algebraic-geometric Riemann theorem for the generalized theta divisor.
Mathematics Subject Classification ID: 11G09
Mathematics Subject Classification ID: 14D20
Mathematics Subject Classification ID: 14K25
zbMATH DE Number: 2153783
zbMATH Keywords: Drinfeld modules
zbMATH Keywords: generalized theta divisor
author: Arturo Álvarez Vazquez
reviewed by: Cicero Carvalho
MaRDI profile type: Publication
full work available at URL: j.jnt.2004.08.006
OpenAlex ID: W1988063741
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DOI: 10.1016/J.JNT.2004.08.006
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description: scientific article; zbMATH DE number 2153783