Ramification filtrations of certain abelian Lie extensions of local fields

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3 Citations (Scopus)

Abstract

Let G ⊂ xFq [x] (q is a power of the prime p) be a subset of formal power series over a finite field such that it forms a compact abelian p-adic Lie group of dimension d ≥ 1. We establish a necessary and sufficient condition for the APF extension of local field corresponding to (Fq(x), G) under the field of norms functor to be an extension of p-adic fields. We then apply this result to study invertible power series over a ring of p-adic integers which commute with a fixed noninvertible power series under composition.

Original languageEnglish
Pages (from-to)135-153
Number of pages19
JournalJournal of Number Theory
Volume168
DOIs
Publication statusPublished - 2016 Nov 1

Keywords

  • Arithmetically profinite extensions
  • Field of norms
  • Formal power series
  • Lubin's conjecture
  • Lubin-Tate formal group
  • P-adic Lie extension
  • Ramification group

ASJC Scopus subject areas

  • Algebra and Number Theory

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