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

Abstract

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Galois groups of local fields, Lie algebras and ramification

“…Then the mixed characteristic case was deduced from it via the Fontaine-Wintenberger field-of-norms functor. In paper [11] we removed the restriction p = 2 and reproved the statement in the context of the pro-p-group Γ K (p).…”

“…Recently, we can treat the general case. First results are related to the case M = 1 and can be found in [11] (we discuss them also in Subsection 3.6 of this paper). The case of arbitrary M as well as the case of higher dimensional local fields will be considered in upcoming papers.…”

“…The modulo p case. In this Subsection we give an overview of the results from [11] related to the modulo p aspect of problems discussed in this paper.…”

“…In [11] we proved that the action of the group ĥ 0 Z/p on f 0 comes from the action of the additive group scheme…”

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

“…Everywhere in the paper p is a prime number, p > 2. In this paper we continue to study the arithmetical structure of the Galois group of complete discrete valuation fields of mixed characteristic initiated in [6].…”