A linear lower bound on the gonality of modular curves
From MaRDI portal
Publication:3128729
DOI10.1155/S1073792896000621zbMath0878.14019arXivalg-geom/9609012OpenAlexW1667760026MaRDI QIDQ3128729
Publication date: 2 June 1997
Published in: International Mathematics Research Notices (Search for Journal in Brave)
Full work available at URL: https://arxiv.org/abs/alg-geom/9609012
elliptic curvesmodular curvesShimura curvesgonalitySelberg's eigenvalue conjecturerational torsiontorsion point of an elliptic curve
Special algebraic curves and curves of low genus (14H45) Elliptic curves (14H52) Kleinian groups (aspects of compact Riemann surfaces and uniformization) (30F40)
Related Items
Pursuing polynomial bounds on torsion ⋮ A criterion to rule out torsion groups for elliptic curves over number fields ⋮ On the Hasse principle for Shimura curves ⋮ Trielliptic modular curves $X_1(N)$ ⋮ Local Diophantine properties of Shimura curves and the \(\overline{\mathbb F}_p\)-gonality ⋮ \(p\)-torsion monodromy representations of elliptic curves over geometric function fields ⋮ Small height and infinite nonabelian extensions ⋮ Unlikely intersections with Hecke translates of a special subvariety ⋮ Computing modular Galois representations ⋮ Trivial points on towers of curves ⋮ On the canonical degrees of curves in varieties of general type ⋮ Automorphisms of Cartan modular curves of prime and composite level ⋮ Measures of irrationality for hypersurfaces of large degree ⋮ Gonality of the modular curve \(X_1(N)\) ⋮ Torsion subgroups of elliptic curves over quintic and sextic number fields ⋮ The local-global principle for divisibility in CM elliptic curves ⋮ Gonality of abstract modular curves in positive characteristic ⋮ The least degree of a CM point on a modular curve ⋮ Gonality of the modular curve 𝑋₀(𝑁) ⋮ Expander graphs, gonality, and variation of Galois representations ⋮ Torsion points on elliptic curves over number fields of small degree ⋮ ON THE AUTOMORPHISMS OF THE NONSPLIT CARTAN MODULAR CURVES OF PRIME LEVEL ⋮ Uniform bounds on the image of the arboreal Galois representations attached to non-CM elliptic curves ⋮ Proving the triviality of rational points on Atkin-Lehner quotients of Shimura curves ⋮ Rational families of 17-torsion points of elliptic curves over number fields ⋮ ABELIAN -DIVISION FIELDS OF ELLIPTIC CURVES AND BRAUER GROUPS OF PRODUCT KUMMER & ABELIAN SURFACES ⋮ On a modular Fermat equation ⋮ The role of the Ramanujan conjecture in analytic number theory ⋮ A combinatorial Li-Yau inequality and rational points on curves ⋮ Asymptotically fast group operations on Jacobians of general curves ⋮ The modularity of elliptic curves over all but finitely many totally real fields of degree 5 ⋮ On the level of modular curves that give rise to isolated \(j\)-invariants ⋮ Bielliptic modular curves \(X_1(M,N)\)
