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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].

MSC:

11G18 Arithmetic aspects of modular and Shimura varieties
11G05 Elliptic curves over global fields
11G09 Drinfel’d modules; higher-dimensional motives, etc.
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