On the \(\mathbb{Q}\)-rational cuspidal subgroup and the component group of \(J_0(p^r)\)

DOI10.1007/BF02760675zbMath0934.14022OpenAlexW2012327714MaRDI QIDQ1366851

San Ling

Publication date: 14 December 1997

Published in: Israel Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/bf02760675

zbMATH Keywords

modular curveAtkin-Lehner involutiondegeneracy mapscuspidal subgroup of the Jacobian

Mathematics Subject Classification ID

Arithmetic ground fields for curves (14H25) Jacobians, Prym varieties (14H40) Modular and Shimura varieties (14G35)

Related Items (15)

Quadratic torsion subgroups of modular Jacobian varieties ⋮ On Eisenstein ideals and the cuspidal group of \(J_{0}(N)\) ⋮ Elliptic curves over totally real quartic fields not containing √5 are modular ⋮ The rational torsion subgroup of \(J_0(N)\) ⋮ Torsion and Tamagawa numbers ⋮ Modular units and cuspidal divisor classes on \(X_0(n^2M)\) with \(n|24\) and \(M\) squarefree ⋮ Quadratic points on modular curves with infinite Mordell–Weil group ⋮ Quadratic points on modular curves ⋮ The \(\mathbb{Q}\)-rational cuspidal group of \(J_{1}(2p)\) ⋮ On spaces of modular forms spanned by eta-quotients ⋮ Component group of the \(p\)-new subvariety of \(J_0 (Mp)\) ⋮ Rational torsion subgroups of modular Jacobian varieties ⋮ On rational Eisenstein primes and the rational cuspidal groups of modular Jacobian varieties ⋮ Rational torsion of generalized Jacobians of modular and Drinfeld modular curves ⋮ The rational cuspidal divisor class group of \(X_0(N)\)

Cites Work

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• Minimal resolution and stable reduction of \(X_ 0(N)\)
• Modular curves and the Eisenstein ideal
• The old subvariety of \(J_ 0(pq)\) and the Eisenstein kernel in Jacobians
• Congruences between cusp forms and the geometry of Jacobians of modular curves
• PARABOLIC POINTS AND ZETA-FUNCTIONS OF MODULAR CURVES
• Hyperelliptic modular curves

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