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On Curves with Many Rational Points over Finite Fields

  • Arnaldo Garcia

Abstract

We summarize results on maximal curves over \({\mathbb{F}_{{q^2}}}\) (i.e., curves attaining the Hasse-Weil upper bound for the number of rational points over finite fields). We discuss the classification problem and the genus spectrum of maximal curves. We present some towers of curves over finite fields attaining the Drinfeld-Vladut bound. Especially interesting is the description of the completely splitting locus (see Formula (20)) of a certain tower of curves, meaning the first description by their coordinates of the supersingular points of the modular curves X 0(2 n ), for each n ∈ ℕ.

Keywords

Rational Point Finite Field Maximal Curve Compositio Math Ramification Point 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Arnaldo Garcia
    • 1
  1. 1.Estrada Dona Castorina, 110IMPARio de JaneiroBrazil

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