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manuscripta mathematica

, Volume 14, Issue 2, pp 173–182 | Cite as

Über das Geschlecht eines inseparablen Funktionenkörpers

  • Henning Stichtenoth
Article

Abstract

Let K/k be an inseparable algebraic function field of one variable of genus g and characteristic p>0. By using constant field extensions it is shown that 2g≥p(p−3)+2 and g≡1(mod p) (for p≠2). Indeed, there exist inseparable function fields with 2g=p(p−3)+2.

Moreover we prove that there is a least constant field extension 1 of k such that L=Kl is separable over 1.

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Literatur

  1. [1]
    DEURING, M.: Lectures on the Theory of Algebraic Functions of One Variable. Lecture Notes in Mathematics 314. Berlin-Heidelberg-New York 1973.Google Scholar
  2. [2]
    KÄHLER, E.: Algebra und Differentialrechnung. Bericht über die Mathematiker-Tagung in Berlin 1953, 58–163.Google Scholar
  3. [3]
    STICHTENOTH, H.: Algebraische Funktionenkörper einer Variablen mit Teilkörpern von beliebig hohem Geschlecht. Erscheint demnächst im Arch. Math.Google Scholar
  4. [4]
    TATE, J.: Genus Change in inseparable Extensions of Function Fields. Proc.Amer. Math. Soc.3, 400–406 (1952).Google Scholar

Copyright information

© Springer-Verlag 1974

Authors and Affiliations

  • Henning Stichtenoth
    • 1
  1. 1.Fakultät für Mathematik und InformatikUniversität Mannheim (WH)

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