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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


Let XD 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 XD,lXD constructed by adding certain level structure at l. The main goal of this note is to study the existence of local points at primes pl 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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