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

TL;DR

This paper extends previous work on algebraic points on Shimura curves of $\

Contribution

It generalizes the classification of algebraic points on Shimura curves of $\

Findings

Finiteness results for algebraic points over higher degree number fields

Similar bounds on elliptic points for large primes p

Extension of previous quadratic field results

Abstract

In the previous article, we classified the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over a quadratic field we showed that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number $p$. In this article, we get a similar result for points over number fields of higher degree on Shimura curves of $\Gamma_0(p)$-type.