A note on algebraic points on Shimura curves

DOI10.1090/conm/701/14147zbMath1440.11102OpenAlexW2792678071MaRDI QIDQ4635399

Keisuke Arai

Publication date: 16 April 2018

Published in: Number Theory Related to Modular Curves (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/conm/701/14147

zbMATH Keywords

rational pointsShimura curvesQM-abelian surfaces

Mathematics Subject Classification ID

Rational points (14G05) Abelian varieties of dimension (> 1) (11G10) Research exposition (monographs, survey articles) pertaining to number theory (11-02) Complex multiplication and moduli of abelian varieties (11G15) Arithmetic aspects of modular and Shimura varieties (11G18)

Cites Work

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• 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 \(\varGamma _0(p)\)-type. III
• Algebraic points on Shimura curves of \(\Gamma_0(p)\)-type
• Errata to ``Algebraic points on Shimura curves of \(\Gamma_0(p)\)-type
• Algebraic points on Shimura curves of \(\Gamma_{0}(p)\)-type. II
• An effective bound of p for algebraic points on Shimura curves of \varGamma₀(p)-type
• On the Rasmussen-Tamagawa conjecture for QM-abelian surfaces
• Points on Shimura curves rational over number fields.
• Les Schémas de Modules de Courbes Elliptiques
• Bounds for the solutions of unit equations

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