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

Yuken Miyasaka; Takao Yamazaki

doi:10.3836/tjm/1391177978

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

Yuken Miyasaka, Takao Yamazaki

Research output: Contribution to journal › Article › peer-review

1 Citation (Scopus)

Abstract

We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hypereiliptic curve given by the equation y ² =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.

Original language	English
Pages (from-to)	387-403
Number of pages	17
Journal	Tokyo Journal of Mathematics
Volume	36
Issue number	2
DOIs	https://doi.org/10.3836/tjm/1391177978
Publication status	Published - 2013 Dec
Externally published	Yes

Keywords

P-adic tau function
Sato grassmannian
Theta divisor
Torsion in jacobian

ASJC Scopus subject areas

Mathematics(all)

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10.3836/tjm/1391177978

Cite this

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title = "Torsion points on hypereiliptic Jacobians via Anderson's p-adic soliton theory",

abstract = "We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hypereiliptic curve given by the equation y 2 =x2g+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.",

keywords = "P-adic tau function, Sato grassmannian, Theta divisor, Torsion in jacobian",

author = "Yuken Miyasaka and Takao Yamazaki",

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AU - Miyasaka, Yuken

AU - Yamazaki, Takao

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N2 - We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hypereiliptic curve given by the equation y 2 =x2g+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.

AB - We show that torsion points of certain orders are not on a theta divisor in the Jacobian variety of a hypereiliptic curve given by the equation y 2 =x2g+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.

KW - P-adic tau function

KW - Sato grassmannian

KW - Theta divisor

KW - Torsion in jacobian

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

Abstract

Keywords

ASJC Scopus subject areas

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