A note on the genus of certain curves over finite fields

Details A note on the genus of certain curves over finite fields A note on the genus of certain curves over finite fields

1995-06-02

arxiv.org/abs/alg-geom/9506003v2

Manuscripta Math. 89 (1996) 103--106

Mathematics

Algebraic Geometry

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

Scientific paper

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 $2g=(q-1)q$.

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