Moscow Mathematical Journal

Volume 16, Issue 2, April–June 2016 pp. 323–370.

Local Points on Shimura Coverings of Shimura Curves at Bad Reduction Primes

Authors: Carlos de Vera-Piquero (1)
Author institution:(1) Fakultät für Mathematik, Universität Duisburg-Essen, Deutschland

Summary:

Let X_D be the Shimura curve associated with an indefinite rational quaternion algebra of reduced discriminant D>1. For each prime l|D, there is a natural cyclic Galois covering of Shimura curves X_D,l → X_D constructed by adding certain level structure at l. The main goal of this note is to study the existence of local points at primes p≠l of bad reduction on the intermediate curves of these coverings and their Atkin–Lehner quotients.

2010 Math. Subj. Class. 11G18, 11G20, 14G05, 14G35.

Keywords: Shimura curves, Atkin–Lehner quotients, coverings, local points.

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