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This article is cited in 3 scientific papers (total in 3 papers)
The Galois group of a multidimensional local field of positive characteristic
O. V. Mel'nikov, A. A. Sharomet
Abstract:
Let $K$ be an arbitrary field, Henselian relative to a discrete valuation $v$ of finite rank $n$ with residue field $k$. If $v=v_n\circ v_{n-1}\circ\dots\circ v_1$, where $v_i$ ($i=1,2,\dots,n$) is a discrete valuation of rank $1$, then, setting $K_n=K$, we denote by $K_{i-1}$ the residue field of the valuation $v_i$ of the field $K_i$, where $i=1,2,\dots,n$. A description of the absolute Galois group $\mathfrak G(K)$ of the field $K$, the inertia group $\mathfrak G^0(K)$ and the ramification group $\mathfrak G^1(K)$ of the valuation $v$ are obtained in terms of the absolute Galois group of the field of residues, its action on the roots of unity in the separable closure of the field $k$, and the cardinalities of the fields $K_0=k$ and $K_1,\dots,K_{n-1}$.
Bibliography: 12 titles.
Received: 21.07.1988
Citation:
O. V. Mel'nikov, A. A. Sharomet, “The Galois group of a multidimensional local field of positive characteristic”, Mat. Sb., 180:8 (1989), 1132–1147; Math. USSR-Sb., 67:2 (1990), 595–610
Linking options:
https://www.mathnet.ru/eng/sm1653https://doi.org/10.1070/SM1990v067n02ABEH002100 https://www.mathnet.ru/eng/sm/v180/i8/p1132
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Abstract page: | 301 | Russian version PDF: | 107 | English version PDF: | 2 | References: | 38 | First page: | 1 |
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