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

2012/02/22 by Arai, Keisuke, Momose, Fumiyuki
#11G18 #14G05 #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.1202.4841

Abstract

In this article, we classify the characters associated to algebraic points on Shimura curves of Γ₀(p)-type, and over a quadratic field we show that there are at most elliptic points on such a Shimura curve for every sufficiently large prime number p. This is an analogue of the study of rational points or points over a quadratic field on the modular curve X₀(p) by Mazur and one of the author (Momose). We also apply the result to a finiteness conjecture on abelian varieties with constrained prime power torsion by Rasmussen-Tamagawa.

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