An effective bound of p for algebraic points on Shimura curves of \varGamma0(p)-type

DOI10.4064/aa164-4-2zbMath1356.11034OpenAlexW2962963409MaRDI QIDQ2875426

Keisuke Arai

Publication date: 14 August 2014

Published in: Acta Arithmetica (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.4064/aa164-4-2

zbMATH Keywords

rational pointsShimura curveseffective boundQM-abelian surfaces

Mathematics Subject Classification ID

Rational points (14G05) Abelian varieties of dimension (> 1) (11G10) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18)

Related Items (3)

Algebraic points on Shimura curves of \(\varGamma _0(p)\)-type. III ⋮ Points on Shimura curves rational over imaginary quadratic fields in the non-split case ⋮ A note on algebraic points on Shimura curves

Cites Work

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• Non-elliptic Shimura curves of genus one
• Rational isogenies of prime degree. (With an appendix by D. Goldfeld)
• On the real points of an arithmetic quotient of a bounded symmetric domain
• A bound for the least prime ideal in the Chebotarev density theorem
• Integral models of certain Shimura curves
• Algebraic points on Shimura curves of \(\Gamma_0(p)\)-type
• Errata to ``Algebraic points on Shimura curves of \(\Gamma_0(p)\)-type
• Points on Shimura curves rational over number fields.

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