A note on the genus of certain curves over finite fields

Rainer Furhmann; Fernando Torres

A note on the genus of certain curves over finite fields

alg-geom 2008-02-03 v2 Algebraic Geometry

Authors: Rainer Furhmann , Fernando Torres

Abstract

We prove the following result which was conjectured by Stichtenoth and Xing: let $g$ be the genus of a projective, irreducible non-singular curve over the finite field $\Bbb F_{q^2}$ and whose number of $\Bbb F_{q^2}$ -rational points attains the Hasse-Weil bound; then either $4g\le (q-1)^2$ or $2g=(q-1)q$ .

Keywords

genus projective curve finite field Hasse-Weil bound rational points

Cite

@article{arxiv.alg-geom/9506003,
  title  = {A note on the genus of certain curves over finite fields},
  author = {Rainer Furhmann and Fernando Torres},
  journal= {arXiv preprint arXiv:alg-geom/9506003},
  year   = {2008}
}

Comments

4 pages, Latex. Reason for resubmission: The proof of the theorem in the previous version of this paper was incomplete

A note on the genus of certain curves over finite fields

Abstract

Keywords

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