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Groups of automorphisms of local fields of period p and nilpotent class < p, I.

Abrashkin, Victor (2017) 'Groups of automorphisms of local fields of period p and nilpotent class < p, I.', International journal of mathematics., 28 (06). p. 1750043.

Abstract

Suppose KK is a finite field extension of Qpℚp containing a primitive ppth root of unity. Let K<pK<p be a maximal pp-extension of KK with the Galois group of period pp and nilpotent class <p<p. In this paper, we develop formalism which allows us to study the structure of Γ<p=Gal(K<p/K)Γ<p=Gal(K<p/K) via methods of Lie theory. In particular, we introduce an explicit construction of a Lie Fp????p-algebra LL and an identification Γ<p=G(L)Γ<p=G(L), where G(L)G(L) is a pp-group obtained from the elements of LL via the Campbell–Hausdorff composition law. In the next paper, we apply this formalism to describe the ramification filtration {Γ(v)<p}v≥0{Γ<p(v)}v≥0 and an explicit form of the Demushkin relation for Γ<pΓ<p.

Item Type:Article
Full text:(AM) Accepted Manuscript
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1142/S0129167X17500434
Publisher statement:Electronic version of an article published as International journal of mathematics, 10.1142/S0129167X17500434 © World Scientific Publishing Company 2017
Date accepted:09 April 2017
Date deposited:09 May 2017
Date of first online publication:23 May 2017
Date first made open access:23 May 2018

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