On curves over finite fields with many rational points

1996/03/14 by Fuhrmann, Rainer, Torres, Fernando
#Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.alg-geom/9603013

Abstract

We study arithmetical and geometrical properties of \it maximal curves, that is, curves defined over the finite field \mathbb F_q² whose number of \mathbb F_q²-rational points reachs the Hasse-Weil upper bound. Under a hypothesis on non-gaps at rational points we prove that maximal curves are \mathbb F_q²-isomorphic to y^q+y=x^m for some m∈ \mathbb Z⁺.

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