Abstract
In this paper, we explore the geometry of the modular curves X 0 (p n), over (Cp in a few non-trivial examples. In particular, we give explicit rigid-analytic parameterizations of the ordinary and supersingular regions. This is done by first building towers of models for X 0 (p n), 0 < i < n, and then pulling back the ordinary and supersingular regions of X(1) via the forgetful maps.
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McMurdy, K. (2004). Explicit Parametrizations of Ordinary and Supersingular Regions of X 0 (p n) . In: Cremona, J.E., Lario, JC., Quer, J., Ribet, K.A. (eds) Modular Curves and Abelian Varieties. Progress in Mathematics, vol 224. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-7919-4_12
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DOI: https://doi.org/10.1007/978-3-0348-7919-4_12
Publisher Name: Birkhäuser, Basel
Print ISBN: 978-3-0348-9621-4
Online ISBN: 978-3-0348-7919-4
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