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Archiv der Mathematik

, Volume 77, Issue 3, pp 241–246 | Cite as

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

  • G. Cornelissen
Article

Abstract.

We determine the exact dimension of the \( {\bf{F}}_2 \)-vector space of \( {\bf{F}}_q \)-rational 2-torsion points in the Jacobian of a hyperelliptic curve over \( {\bf{F}}_q \) (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.

Keywords

Vector Space Genus Theory Finite Field Function Field Rational Factor 

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Copyright information

© Birkhäuser Verlag, Basel 2001

Authors and Affiliations

  • G. Cornelissen
    • 1
    • 2
  1. 1.Max-Planck-Institut für Mathematik, Vivatsgasse 7, D-53111 BonnGermany
  2. 2.University of Gent, Department of Pure Mathematics, Galglaan 2, B-9000 Gent, gc@cage.rug.ac.beBelgium

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