On ramification in the compositum of function fields

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Anbar, Nurdagül and Stichtenoth, Henning and Tutdere, Seher (2009) On ramification in the compositum of function fields. Bulletin of the Brazilian Mathematical Society, 40 (4). pp. 539-552. ISSN 1678-7544 (Print) 1678-7714 (Online)

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The aim of this paper is twofold: Firstly, we generalize well-known formulas for ramification and different exponents in cycle extensions of function fields over a field K (due to H. Hasse) to extensions E = F (y), where y satisfies an equation of f (y) = u . g (y) with polynomials f (y), g (y) is an element of K [y] and u is an element of F. This result depends essentially on Abhyankar's Lemma which gives information about ramification in a compositum E = E1E2 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 widly ramified. Our second objective is a generalization of Abhyankar's Lemma 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.
Item Type: Article
Uncontrolled Keywords: function fields; ramification; Abhyankar's Lemma
Subjects: Q Science > QA Mathematics
Divisions: Faculty of Engineering and Natural Sciences
Depositing User: Henning Stichtenoth
Date Deposited: 02 Nov 2009 14:05
Last Modified: 23 Jul 2019 14:27
URI: https://research.sabanciuniv.edu/id/eprint/12446

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