Number theory seminar in memory of F. Momose

Algebraic points on Shimura curves of $\Gamma_0(p)$-type


Keisuke Arai


We classify the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over number fields (not only quadratic fields but also fields of higher degree) we show that there are few points on such a Shimura curve for every suficiently large prime number p. This is an analogue of the study of rational points or points over quadratic fields on the modular curve $X_0(p)$ by Mazur and Momose.


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