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manuscripta mathematica

, Volume 72, Issue 1, pp 67–79 | Cite as

Elementary Abelianp-extensions of algebraic function fields

  • Arnaldo Garcia
  • Henning Stichtenoth
Article

Abstract

LetK be a field of characteristicp>0 andF/K be an algebraic function field. We obtain several results on Galois extensionsE/F with an elementary Abelian Galois group of orderp n.
  1. (a)

    E can be generated overF by some elementy whose minimal polynomial has the specific formT pnTz.

     
  2. (b)

    A formula for the genus ofE is given.

     
  3. (c)

    IfK is finite, then the genus ofE grows much faster than the number of rational points (as [EF] → ∞).

     
  4. (d)

    We present a new example of a function fieldE/K whose gap numbers are nonclassical.

     

Keywords

Function Field Algebraic Curf Minimal Polynomial Galois Extension Constant Field 
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 1991

Authors and Affiliations

  • Arnaldo Garcia
    • 1
  • Henning Stichtenoth
    • 2
  1. 1.Pura e AplicadaInstituto de MatematicaRio de JaneiroBrazil
  2. 2.Fachbereich 6-MathematikUniversität GHS EssenEssen 1Fed. Rep. Germany

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