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Extensions of local fields and truncated power series

✍ Scribed by Kevin Keating

Publisher
Elsevier Science
Year
2006
Tongue
English
Weight
383 KB
Volume
116
Category
Article
ISSN
0022-314X

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✦ Synopsis

Let K be a finite tamely ramified extension of Q p and let L/K be a totally ramified (Z/p n Z)-extension. Let L be a uniformizer for L, let be a generator for Gal(L/K), and let f (X) be an element of O K [X] such that ( L ) = f ( L ). We show that the reduction of f (X) modulo the maximal ideal of O K determines a certain subextension of L/K up to isomorphism. We use this result to study the field extensions generated by periodic points of a p-adic dynamical system.

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