On ramification in the compositum of function fields

  • Nurdagül Anbar
  • Henning Stichtenoth
  • Seher Tutdere
Article

Abstract

The aim of this paper is twofold: Firstly, we generalize well-known formulas for ramification and different exponents in cyclic extensions of function fields over a field K (due to H. Hasse) to extensions E = F(y), where y satisfies an equation of the form f(y) = u · g(y) with polynomials f(y), g(y) ∈ K[y] and uF. This result depends essentially on Abhyankar’s Lemma which gives information about ramification in a compositum E = E1E2 of finite extensions E1, E2 over a function field F. Abhyankar’s Lemma does not hold if both extensions E1/F and E2/F are wildly ramified. Our second objective is a generalization of Abhyankar’s Lemma if E1/F and E2/F are cyclic extensions of degree p = char(K). This result may be useful for the study of wild towers of function fields over finite fields.

Keywords

function fields ramification Abhyankar’s Lemma 

Mathematical subject classification

14H05 14G15 11R58 

Copyright information

© Springer 2009

Authors and Affiliations

  • Nurdagül Anbar
    • 1
  • Henning Stichtenoth
    • 1
  • Seher Tutdere
    • 1
  1. 1.MDBF, OrhanlıSabancı UniversityTuzla, İstanbulTurkey

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