Minimal models for Drinfeld modules of rank 2 with complex multiplication
type: Item
instance of: scholarly article
title: Minimal models for Drinfeld modules of rank 2 with complex multiplication
zbMATH Open document ID: 0959.11025
author: Sunghan Bae
author: Daeyeol Jeon
published in: Archiv der Mathematik
publication date: 2001-04-29T00:00:00Z
review text: This paper continues the first author's paper [Pac. J. Math. 167, 215-230 (1995; Zbl 0826.11025)] on Drinfeld modules with complex multiplication and Hecke characters. Let \(\phi\) be a rank 2 Drinfeld \({\mathbb F}_q[T]\)-module with CM by the maximal order of a separable, imaginary quadratic extension \(K\) of \(k={\mathbb F}_q(T)\), and suppose that \(\phi\) is defined over the Hilbert class field \(H\) of \(K\). In analogy with \(\mathbb Q\)-curves in the theory of elliptic curves, such a Drinfeld module is called a \(k\)-module if it is \(H\)-isogenous to all its \(Gal(H/k)\)-conjugates. The main result is that certain \(k\)-modules \(\phi\) have a global minimal model over \(k(j(\phi))\). For the corresponding result on \(\mathbb Q\)-curves see \textit{B. Gross} [Compos. Math. 45, 155-164 (1982; Zbl 0541.14010)].
reviewed by: Andreas Schweizer
Mathematics Subject Classification ID: 11G09
zbMATH DE Number: 1449199
zbMATH Keywords: Drinfeld module
zbMATH Keywords: complex multiplication
zbMATH Keywords: Hecke character
zbMATH Keywords: global minimal model
MaRDI profile type: Publication
full work available at URL: s000130050430
OpenAlex ID: W2003507014
DOI: 10.1007/S000130050430
description: scientific article; zbMATH DE number 1449199