JP Journal of Algebra, Number Theory and Applications
Volume 37, Issue 1, Pages 69 - 104
(August 2015) http://dx.doi.org/10.17654/JPANTAAug2015_069_104 |
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WILD RAMIFICATION IN A FAMILY OF LOW-DEGREE EXTENSIONS ARISING FROM ITERATION
Benjamin Breen, Rafe Jones, Tommy Occhipinti and Michelle Yuen
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Abstract: This article gives a first look at wild ramification in a family of iterated extensions. For we consider the splitting field of the second iterate of We give complete information on the factorization of the ideal (2) as c varies, and find a surprisingly complicated dependence of this factorization on the parameter c. We show that 2 ramifies (necessarily wildly) in all these extensions except when and we describe the higher ramification groups in some totally ramified cases. |
Keywords and phrases: ramification, number fields, polynomial iteration, ideal factorization. |
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