Two-torsion in the Jacobian of hyperelliptic curves over finite fields

Gunther Cornelissen

doi:10.1007/PL00000487

Two-torsion in the Jacobian of hyperelliptic curves over finite fields

Gunther Cornelissen^*

^*Corresponding author for this work

Sub Fundamental Mathematics

extern

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

Abstract

Abstract. We determine the exact dimension of the F₂-vector space of F_q-rational 2-torsion points in the Jacobian of a hyperelliptic curve over F_q (q odd) in terms of the degrees of the rational factors of its discriminant, and relate this to genus theory for the corresponding function field. As a corollary, we prove the existence of a point of order > 2 in the Jacobian of certain real hyperelliptic curves.

Original language	English
Pages (from-to)	241-246
Number of pages	6
Journal	Archiv der Mathematik
Volume	77
Issue number	3
DOIs	https://doi.org/10.1007/PL00000487
Publication status	Published - 3 Sept 2001

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abstract = "Abstract. We determine the exact dimension of the F2-vector space of Fq-rational 2-torsion points in the Jacobian of a hyperelliptic curve over Fq (q odd) in terms of the degrees of the rational factors of its discriminant, and relate this to genus theory for the corresponding function field. As a corollary, we prove the existence of a point of order > 2 in the Jacobian of certain real hyperelliptic curves.",

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AB - Abstract. We determine the exact dimension of the F2-vector space of Fq-rational 2-torsion points in the Jacobian of a hyperelliptic curve over Fq (q odd) in terms of the degrees of the rational factors of its discriminant, and relate this to genus theory for the corresponding function field. As a corollary, we prove the existence of a point of order > 2 in the Jacobian of certain real hyperelliptic curves.

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Two-torsion in the Jacobian of hyperelliptic curves over finite fields

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