Local points on Shimura coverings of Shimura curves at bad reduction primes
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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,l → XD 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.
Citationde Vera-Piquero, C. Local points on Shimura coverings of Shimura curves at bad reduction primes. "Moscow Mathematical Journal", 2016, vol. 16, núm. 2, p. 323-370.