Galois groups of local fields, Lie algebras and ramification

Abrashkin, Victor

doi:10.1017/cbo9781316106877.006

Cited by 9 publications

(7 citation statements)

References 16 publications

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“…The above result is a covariant version of the nilpotent Artin-Schreier theory developed in [2], cf. also Subsection 1.1 in [7] for the relation between the covariant and contravariant versions of this theory and for appropriate non-formal comments.…”

Section: Preliminariesmentioning

confidence: 99%

“…The covariant version of the Witt-Artin-Schreier theory [2], Section 1 (cf. also [7], Subsection 1.1 and [8], Section 1), gives explicit description of the automorphisms η <p,0 in terms of the identification η M . Consider a special case of this construction when η 0 admits a lift η ∈ Aut O(K) which commutes with σ, and therefore we have the appropriate lifts η <p ∈ Aut O(K <p ), cf.…”

Section: Preliminariesmentioning

confidence: 99%

“…is a profinite Lie Z/p M -algebra of nilpotent class < p and G(L) is the pro-p-group, obtained from L by the Campbell-Hausdorff composition law, cf. Subsection 1.2 below for more details and Subsection 1.1 in [7] for non-formal comments about nilpotent Artin-Schreier theory.…”

Section: Introductionmentioning

confidence: 99%

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Automorphisms of local fields of period $p^M$ and nilpotent class $

Abrashkin

2015

Preprint

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Suppose K is a finite extension of Q p containing a p M -th primitive root of unity. For 1 s < p denote by K[s, M ] the maximal p-extension of K with the Galois group of period p M and nilpotent class s. We apply the nilpotent Artin-Schreier theory together with the theory of the field-of-norms functor to give an explicit description of the Galois groups Gal(K[s, M ]/K). As application we prove that the ramification subgroup Γ (v) K of the absolute Galois group of K acts trivially on K[s, M ] if and only if v > e K (M + s/(p − 1)) − (1 − δ 1s )/p, where e K is the ramification index of K and δ 1s is the Kronecker symbol.

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Section: Preliminariesmentioning

confidence: 99%

Section: Preliminariesmentioning

confidence: 99%

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Automorphisms of local fields of period $p^M$ and nilpotent class $

Abrashkin

2015

Preprint

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“…In [1,2] we developed a nilpotent analogue of the classical Artin-Schreier theory of cyclic field extensions of characteristic p. We are going to use the covariant analog of this theory, cf. the discussion in [7], for explicit description of the group G <p = G/G p C p (G) as follows.…”

Section: Preliminariesmentioning

confidence: 99%

“…These subgroups reflect arithmetic structure on G <p , cf. motivation in [7]. First results about these ramification subgroups were obtained by the author in [1].…”

Section: Introductionmentioning

confidence: 98%

A ramification filtration of the Galois group of a local field

Abrashkin¹

1995

Proceedings of the St. Petersburg Mathematical Society Volume III

100

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Let K be a field of formal Laurent series with coefficients in a finite field of characteristic p, G

0 we construct epimorphism of Lie algebrasη † : L −→L † and the action Ω U of the formal group α p = Spec F p [U ], U p = 0, of order p onL † . Suppose dΩ U = B † U , where B † ∈ DiffL † , and L † [v 0 ] is the ideal ofL † generated by the elements of B † (L † ). The main result of the paper states that L (v0) = (η † ) −1L † [v 0 ]. In the last sections we relate this result to the explicit construction of generators of L (v0) obtained earlier by the author and develop its more efficient version.

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An Introduction to p-Adic Hodge Theory

Benois

2022

Infosys Science Foundation Series

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Galois groups of local fields, Lie algebras and ramification

Cited by 9 publications

References 16 publications

Automorphisms of local fields of period $p^M$ and nilpotent class $

Automorphisms of local fields of period $p^M$ and nilpotent class $

A ramification filtration of the Galois group of a local field

An Introduction to p-Adic Hodge Theory

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