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On ramification filtrations and p-adic differential equations, II: mixed characteristic case

Part of: Differential and difference algebra Algebraic number theory: local and $p$-adic fields

Published online by Cambridge University Press:  30 November 2011

Liang Xiao
Liang Xiao*
Affiliation:
Department of Mathematics, University of Chicago, 5734 S. University Avenue, Chicago, IL 60637, USA (email: lxiao@math.uchicago.edu)
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Abstract

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Let K be a complete discrete valuation field of mixed characteristic (0,p), with possibly imperfect residue field. We prove a Hasse–Arf theorem for the arithmetic ramification filtrations on GK, except possibly in the absolutely unramified and non-logarithmic case, or the p=2 and logarithmic case. As an application, we obtain a Hasse–Arf theorem for filtrations on finite flat group schemes over 𝒪K.

Keywords

ramificationp-adic differential equationsimperfect residue fields

MSC classification

Secondary: 11S15: Ramification and extension theory 12H25: $p$-adic differential equations
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 2 , March 2012 , pp. 415 - 463
Copyright
Copyright © Foundation Compositio Mathematica 2011

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