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On curves over finite fields with many rational points

Rainer Fuhrmann·Fernando Torres
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Abstract

We study arithmetical and geometrical properties of {\it maximal curves}, that is, curves defined over the finite field $\mathbb F_{q^2}$ whose number of $\mathbb F_{q^2}$-rational points reachs the Hasse-Weil upper bound. Under a hypothesis on non-gaps at rational points we prove that maximal curves are $\mathbb F_{q^2}$-isomorphic to $y^q+y=x^m$ for some $m\in \mathbb Z^+$.

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BibTeXRIS

Rainer Fuhrmann, Fernando Torres. 1996-03-14. On curves over finite fields with many rational points. https://arxiv.org/abs/alg-geom/9603013

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