Algebraic points on Shimura curves of Γ₀(p)-type (II)

2012/05/16 by Keisuke Arai, Arai, Keisuke · 2 citations
Mathematics · Social Sciences · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #Vietnamese History and Culture Studies #math.NT #msc:11G10 #msc:11G15 #msc:11G18 #msc:14G05

paper · pdf · doi:10.48550/arxiv.1205.3596

11 pages. arXiv admin note: substantial text overlap with arXiv:1202.4841

arxiv created 2012/10/30 · arxiv updated 2012/10/31

Abstract

In the previous article, we classified the characters associated to algebraic points on Shimura curves of Γ₀(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 Γ₀(p)-type.

Citations

• Algebraic points on Shimura curves of Γ₀(p)-type

Cited by

• An effective bound of p for algebraic points on Shimura curves of Γ₀(p)-type
• Algebraic points on Shimura curves of Γ₀(p)-type (III)

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