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arXiv:1303.5270 [math.NT]AbstractReferencesReviewsResources

Algebraic points on Shimura curves of $Γ_0(p)$-type (III)

Keisuke Arai

Published 2013-02-22Version 1

In previous articles, we classified the characters associated to algebraic points on Shimura curves of $\Gamma_0(p)$-type, and over number fields in a certain large class 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 prove the non-existence of elliptic points on Shimura curves of $\Gamma_0(p)$-type under a mild assumption. We also give an explicit example.

Comments: 11 pages. arXiv admin note: substantial text overlap with arXiv:1211.0129, arXiv:1205.3596, arXiv:1202.4841
Categories: math.NT
Subjects: 11G18, 14G05, 11G10, 11G15
Related articles: Most relevant | Search more
arXiv:1205.3596 [math.NT] (Published 2012-05-16, updated 2012-10-30)
Algebraic points on Shimura curves of $Γ_0(p)$-type (II)
arXiv:1202.4841 [math.NT] (Published 2012-02-22, updated 2012-10-29)
Algebraic points on Shimura curves of $Γ_0(p)$-type
arXiv:1211.0129 [math.NT] (Published 2012-11-01, updated 2012-12-27)
An effective bound of $p$ for algebraic points on Shimura curves of $Γ_0(p)$-type

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