Rational torsion of generalised modular Jacobians of odd level

2021/12/07 by Mar Curcó Iranzo, Iranzo, Mar Curcó
Mathematics · #11G16 #11G18 (14H40 #11G45 #14G05) #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)

paper · pdf · doi:10.48550/arxiv.2112.03741

openalex publication_date 2021/12/07 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We consider the generalised Jacobian J₀(N)_m of the modular curve X₀(N) of level N, with respect to the modulus m consisting of all cusps on the modular curve. When N is odd, we determine the group structure of the rational torsion J₀(N)_m(ℚ)_tor up to 2-primary and l-primary parts for any prime l dividing N. Our results extend those of Wei--Yamazaki for squarefree levels and Yamazaki--Yang for prime-power levels.

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