### Abstract

Let G ⊂ xF_{q} [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 (F_{q}(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 language | English |
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Pages (from-to) | 135-153 |

Number of pages | 19 |

Journal | Journal of Number Theory |

Volume | 168 |

DOIs | |

Publication status | Published - 2016 Nov 1 |

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### 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

### Cite this

**Ramification filtrations of certain abelian Lie extensions of local fields.** / Hsia, Liang-Chung; Li, Hua-Chieh.

Research output: Contribution to journal › Article

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TY - JOUR

T1 - Ramification filtrations of certain abelian Lie extensions of local fields

AU - Hsia, Liang-Chung

AU - Li, Hua-Chieh

PY - 2016/11/1

Y1 - 2016/11/1

N2 - 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.

AB - 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.

KW - Arithmetically profinite extensions

KW - Field of norms

KW - Formal power series

KW - Lubin's conjecture

KW - Lubin-Tate formal group

KW - P-adic Lie extension

KW - Ramification group

UR - http://www.scopus.com/inward/record.url?scp=84973109199&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84973109199&partnerID=8YFLogxK

U2 - 10.1016/j.jnt.2016.04.008

DO - 10.1016/j.jnt.2016.04.008

M3 - Article

AN - SCOPUS:84973109199

VL - 168

SP - 135

EP - 153

JO - Journal of Number Theory

JF - Journal of Number Theory

SN - 0022-314X

ER -