Bulletin of the Brazilian Mathematical Society, New Series

, 40:539

On ramification in the compositum of function fields

Authors

    • MDBF, OrhanlıSabancı University
  • Henning Stichtenoth
    • MDBF, OrhanlıSabancı University
  • Seher Tutdere
    • MDBF, OrhanlıSabancı University
Article

DOI: 10.1007/s00574-009-0026-8

Cite this article as:
Anbar, N., Stichtenoth, H. & Tutdere, S. Bull Braz Math Soc, New Series (2009) 40: 539. doi:10.1007/s00574-009-0026-8

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 fieldsramificationAbhyankar’s Lemma

Mathematical subject classification

14H0514G1511R58

Copyright information

© Springer 2009