Extensions of local fields and truncated power series

2003/12/19 by Kevin Keating, Keating, Kevin
Mathematics · #11S15 #Algebraic Geometry and Number Theory #FOS: Mathematics #Mathematical Dynamics and Fractals #Number Theory (math.NT) #advanced mathematical theories #math.NT #msc:11S15

paper · pdf · doi:10.48550/arxiv.math/0312391

29 pages

openalex publication_date 2003/12/19 · arxiv created 2005/03/16 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let K be a finite tamely ramified extension of \Q_p and let L/K be a totally ramified (\Z/pⁿ\Z)-extension. Let π_L be a uniformizer for L, let σ be a generator for \Gal(L/K), and let f(X) be an element of Ø_K[X] such that σ(π_L)=f(π_L). We show that the reduction of f(X) modulo the maximal ideal of Ø_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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