Torsion points on hyperelliptic Jacobians via Anderson's p-adic soliton theory

2011/11/12 by Yuken Miyasaka, Takao Yamazaki, Miyasaka, Yuken +1
Mathematics · #Advanced Algebra and Geometry #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #math.NT

paper · pdf · doi:10.48550/arxiv.1111.2973

16 pages

openalex publication_date 2011/11/12 · arxiv created 2012/06/28 · arxiv updated 2012/06/29 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hyperelliptic curve given by the equation y²=x^2g+1+x with g ≥ 2. The proof employs a method of Anderson who proved an analogous result for a cyclic quotient of a Fermat curve of prime degree.

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