On ramification in the compositum of function fields

Nurdagül Anbar Meidl, Henning Stichtenoth, Seher Tutdere

Research output: Contribution to journalJournal articleResearchpeer-review

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 u ∈ F. This result depends essentially on Abhyankar’s Lemma which gives information about ramification in a compositum E = E 1 E 2 of finite extensions E 1, E 2 over a function field F. Abhyankar’s Lemma does not hold if both extensions E 1/F and E 2/F are wildly ramified. Our second objective is a generalization of Abhyankar’s Lemma if E 1/F and E 2/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.
Original languageEnglish
JournalBulletin of the Brazilian Mathematical Society, New Series
Volume40
Issue number4
Pages (from-to)539-552
ISSN1678-7544
DOIs
Publication statusPublished - 2009
Externally publishedYes

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