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On Schottky coverings of Drinfeld modular curves. (Sur les revêtements de Schottky des courbes modulaires de Drinfeld.) (French) Zbl 0853.14014
Drinfeld modular curves are Mumford curves at \(\infty\). We give explicit Schottky coverings for them. The most important fact is that, if \(M_\Gamma\) is the (affine) modular curve associated to the arithmetic group \(\Gamma\), then a Schottky group for \(\overline M_\Gamma\) (the canonical completion of \(M_\Gamma)\) appears to be a subgroup of \(\Gamma\), indeed its free part.

14H30 Coverings of curves, fundamental group
14G20 Local ground fields in algebraic geometry
11G30 Curves of arbitrary genus or genus \(\ne 1\) over global fields
11G09 Drinfel’d modules; higher-dimensional motives, etc.
Full Text: DOI
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