NDLI: On ramification in the compositum of function fields

Content Provider	Springer Nature Link
Author	Anbar, Nurdagül Stichteth, Henning Tutdere, Seher
Copyright Year	2009
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.
Ending Page	552
Page Count	14
Starting Page	539
File Format	PDF
ISSN	16787544
e-ISSN	16787714
Journal	Bulletin of the Brazilian Mathematical Society
Issue Number	4
Volume Number	40
Language	English
Publisher	Springer-Verlag
Publisher Date	2009-11-10
Publisher Place	Berlin, Heidelberg
Access Restriction	One Nation One Subscription (ONOS)
Subject Keyword	function fields Abhyankar’s Lemma Theoretical, Mathematical and Computational Physics Algebraic functions; function fields Finite ground fields Mathematics Arithmetic theory of algebraic function fields ramification
Content Type	Text
Resource Type	Article
Subject	Mathematics

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