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A note on the genus of certain curves over finite fields

Rainer Furhmann·Fernando Torres
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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 $2g=(q-1)q$.

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BibTeXRIS

Rainer Furhmann, Fernando Torres. 1995-10-21. A note on the genus of certain curves over finite fields. https://arxiv.org/abs/alg-geom/9506003

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