2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/147141We 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 $2g=(q-1)q$.4 pages, Latex. Reason for resubmission: The proof of the theorem in the previous version of this paper was incompleteAlgebraic Geometrytext