Schweizer, Andreas Hyperelliptic Drinfeld modular curves. (English) Zbl 0930.11039 Gekeler, E.-U. (ed.) et al., Proceedings of the workshop on Drinfeld modules, modular schemes and applications, Alden-Biesen, Belgium, September 9–14, 1996. Singapore: World Scientific. 330-343 (1997). The author shows that for all \({\mathfrak p}\in\mathbb{F}_q[T]\), the Drinfeld modular curve \(X_0({\mathfrak p})\) is “conservative” in that all constant field extensions of its function field are genus-preserving. The author then determines all \({\mathfrak p}\) for which \(X_0({\mathfrak p})\) is rational, elliptic, or hyperelliptic.For the entire collection see [Zbl 0897.00023]. Reviewer: D.Goss (Columbus/Ohio) Cited in 2 ReviewsCited in 16 Documents MSC: 11G18 Arithmetic aspects of modular and Shimura varieties 11G05 Elliptic curves over global fields 11G09 Drinfel’d modules; higher-dimensional motives, etc. Keywords:rational curves; elliptic curves; hyperelliptic curves; Drinfeld modular curve; constant field extensions; genus-preserving PDFBibTeX XMLCite \textit{A. Schweizer}, in: Proceedings of the workshop on Drinfeld modules, modular schemes and applications, Alden-Biesen, Belgium, September 9--14, 1996. Singapore: World Scientific. 330--343 (1997; Zbl 0930.11039)