2015/02/24 by Liang-Chung Hsia, Hsia, Liang-Chung, Hua-Chieh Li +1
Mathematics · #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Number Theory (math.NT) #advanced mathematical theories #math.NT
paper · pdf · doi:10.48550/arxiv.1502.06815
arxiv created 2015/02/24 · openalex publication_date 2015/02/24 · arxiv updated 2015/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G⊂ x\mathbb Fq[ [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 (\mathbb Fq( (x) ), G) under the field of norms functor to be an extension of p-adic fields. We then apply this result to study family of invertible power series with coefficients in a p-adic integers ring and commute with a fixed noninvertible power series under the composition of power series.