A characterization of strictly APF extensions

Bryden Cais; Christopher Davis; Jonathan Lubin

doi:10.5802/jtnb.946

A characterization of strictly APF extensions

Bryden Cais, Christopher Davis, Jonathan Lubin

Mathematics

Research output: Contribution to journal › Article › peer-review

4 Scopus citations

Abstract

Let K denote a finite extension of Q_p. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine- Wintenberger. Our conditions are phrased in terms of the existence of a certain tower of intermediate subfields. These conditions are well-suited to producing examples of strictly APF extensions, and in particular, our main theorem proves that the φ-iterate extensions previously considered by the first two authors are strictly APF.

Original language	English (US)
Pages (from-to)	417-430
Number of pages	14
Journal	Journal de Theorie des Nombres de Bordeaux
Volume	28
Issue number	2
DOIs	https://doi.org/10.5802/jtnb.946
State	Published - 2016

Keywords

Arithmetically profinite extensions
Non-Archimedean dynamical systems
Ramification theory

ASJC Scopus subject areas

Algebra and Number Theory

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10.5802/jtnb.946

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abstract = "Let K denote a finite extension of Qp. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine- Wintenberger. Our conditions are phrased in terms of the existence of a certain tower of intermediate subfields. These conditions are well-suited to producing examples of strictly APF extensions, and in particular, our main theorem proves that the φ-iterate extensions previously considered by the first two authors are strictly APF.",

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author = "Bryden Cais and Christopher Davis and Jonathan Lubin",

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AU - Cais, Bryden

AU - Davis, Christopher

AU - Lubin, Jonathan

PY - 2016

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N2 - Let K denote a finite extension of Qp. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine- Wintenberger. Our conditions are phrased in terms of the existence of a certain tower of intermediate subfields. These conditions are well-suited to producing examples of strictly APF extensions, and in particular, our main theorem proves that the φ-iterate extensions previously considered by the first two authors are strictly APF.

AB - Let K denote a finite extension of Qp. We give necessary and sufficient conditions for an infinite totally wildly ramified extension L/K to be strictly APF in the sense of Fontaine- Wintenberger. Our conditions are phrased in terms of the existence of a certain tower of intermediate subfields. These conditions are well-suited to producing examples of strictly APF extensions, and in particular, our main theorem proves that the φ-iterate extensions previously considered by the first two authors are strictly APF.

KW - Arithmetically profinite extensions

KW - Non-Archimedean dynamical systems

KW - Ramification theory

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JF - Journal de Theorie des Nombres de Bordeaux

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ER -

A characterization of strictly APF extensions

Abstract

Keywords

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