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The genus of curves over finite fields with many rational points

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Abstract

We prove the following result which was conjectured by Stichtenoth and Xing: letg be the genus of a projective, irreducible non-singular algebraic curve over the finite field\(\mathbb{F}_{q^2 } \) and whose number of\(\mathbb{F}_{q^2 } \)-rational points attains the Hasse-Weil bound; then either 4g≤(q−1)2 or 2g=(q−1)q.

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Authors and Affiliations

  1. Fachbereich 6, Mathematik und Informatik, Universität Essen, D-45117, Essen, Germany

    Rainer Fuhrmann

  2. Mathematics Section, ICTP, P.O. Box 586, 34100, Trieste, Italy

    Fernando Torres

Authors
  1. Rainer Fuhrmann
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  2. Fernando Torres
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Supported by a grant from the International Atomic Energy and UNESCOCorrespondence to: F. Torres

This article was processed by the author using theLatex style file from Springer-Verlag.

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Fuhrmann, R., Torres, F. The genus of curves over finite fields with many rational points. Manuscripta Math 89, 103–106 (1996). https://doi.org/10.1007/BF02567508

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