Local diophantine properties of Shimura curves

DOI10.1007/BF01456184zbMath0536.14018WikidataQ104439613 ScholiaQ104439613MaRDI QIDQ791586

Ron A. Livné, Bruce W. Jordan

Publication date: 1985

Published in: Mathematische Annalen (Search for Journal in Brave)

Full work available at URL: https://eudml.org/doc/182956

zbMATH Keywords

Shimura curvesno points over nonarchimedean local fields

Mathematics Subject Classification ID

Rational points (14G05) Arithmetic ground fields for curves (14H25) Special algebraic curves and curves of low genus (14H45) Local ground fields in algebraic geometry (14G20) (p)-adic and power series fields (11D88)

Related Items (26)

Descent on certain Shimura curves ⋮ Explicit Connections Between Supersingular Isogeny Graphs and Bruhat–Tits Trees ⋮ On the Birch and Swinnerton-Dyer conjecture for modular elliptic curves over totally real fields ⋮ Local Diophantine properties of Shimura curves and the \(\overline{\mathbb F}_p\)-gonality ⋮ Shimura curves as intersections of Humbert surfaces and defining equations of QM-curves of genus two ⋮ Non-elliptic Shimura curves of genus one ⋮ Mumford curves covering 𝑝-adic Shimura curves and their fundamental domains ⋮ Integral Hodge theory and congruences between modular forms ⋮ Les courbes de Shimura ⋮ Powers of 2 in modular degrees of modular abelian varieties ⋮ \(\mathcal D\)-elliptic sheaves and odd Jacobians ⋮ 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 \(p\)-adic Maass-Shimura operator on Mumford curves ⋮ On the anticyclotomic Iwasawa main conjecture for Hilbert modular forms of parallel weights ⋮ Generalized Heegner cycles on Mumford curves ⋮ On a theorem of Bertolini-Darmon on the rationality of Stark-Heegner points over genus fields of real quadratic fields ⋮ Exceptional zero formulae for anticyclotomic \(p\)-adic \(L\)-functions of elliptic curves in the ramified case ⋮ Euler system obtained from congruences between Hilbert modular forms ⋮ Shimura curve quotients with odd Jacobians ⋮ From the Taniyama-Shimura conjecture to Fermat's last theorem ⋮ The Shimura covering of a Shimura curve: automorphisms and étale subcoverings ⋮ Discrete groups, Mumford curves and theta functions ⋮ Unnamed Item ⋮ Drinfeld-Stuhler modules ⋮ Local diophantine properties of modular curves of 𝒟-elliptic sheaves

Cites Work

• On the real points of an arithmetic quotient of a bounded symmetric domain
• Hecke polynomials as congruence \(\zeta\) functions in elliptic modular case
• Construction of class fields and zeta functions of algebraic curves
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