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
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Stichtenoth, H. Über das Geschlecht eines inseparablen Funktionenkörpers. Manuscripta Math 14, 173–182 (1974). https://doi.org/10.1007/BF01171440
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DOI: https://doi.org/10.1007/BF01171440