Points on Shimura curves rational over number fields.

DOI10.1515/crll.1986.371.92zbMath0587.14018OpenAlexW100581404MaRDI QIDQ3714182

Bruce W. Jordan

Publication date: 1986

Published in: Journal für die reine und angewandte Mathematik (Crelles Journal) (Search for Journal in Brave)

Full work available at URL: https://www.digizeitschriften.de/dms/resolveppn/?PPN=GDZPPN002203944

zbMATH Keywords

quaternionic multiplicationimaginary quadratic number fieldQM-abelian surfacespotential good reductionfew rational points of Shimura curve

Mathematics Subject Classification ID

Quadratic extensions (11R11) Rational points (14G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45)

Related Items (17)

Descent on certain Shimura curves ⋮ On the Hasse principle for Shimura curves ⋮ Algebraic points on Shimura curves of \(\Gamma_{0}(p)\)-type. II ⋮ Algebraic points on Shimura curves of \(\varGamma _0(p)\)-type. III ⋮ Rational points on Atkin-Lehner quotients of geometrically hyperelliptic Shimura curves ⋮ Points on Shimura curves rational over imaginary quadratic fields in the non-split case ⋮ A note on algebraic points on Shimura curves ⋮ Examples of abelian surfaces failing the local-global principle for isogenies ⋮ The arithmetic of QM-abelian surfaces through their Galois representations ⋮ On QM-abelian surfaces with model of GL\(_{2}\)-type over \(\mathbb Q\) ⋮ Non-existence of points rational over number fields on Shimura curves ⋮ The Shimura covering of a Shimura curve: automorphisms and étale subcoverings ⋮ Examples of genuine QM abelian surfaces which are modular ⋮ Drinfeld-Stuhler modules ⋮ RATIONAL POINTS ON SHIMURA CURVES AND THE MANIN OBSTRUCTION ⋮ Surface abéliennes à multiplication quaternionique munie d'une structure de niveau Γ₀(N) ⋮ An effective bound of p for algebraic points on Shimura curves of \varGamma₀(p)-type

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