On just infinite pro-p-groups and arithmetically profinite extensions of local fields

Details On just infinite pro-p-groups and arithmetically profinite extensions of local fields On just infinite pro-p-groups and arithmetically profinite extensions of local fields

1998-02-19

arxiv.org/abs/math/9802092v1

Mathematics

Group Theory

15 pages, AMSTeX

Scientific paper

The wild group is the group of wild automorphisms of a local field of characteristic p. In this paper we apply Fontaine-Wintenberger's theory of fields of norms to study the structure of the wild group. In particular we provide a new short proof of R. Camina's theorem which says that every pro-p-group with countably many open sugroups is isomorphic to a closed subgroup of the wild group. We study some closed subgroups T of the wild group whose commutator subgroup is unusually small. Realizing the group T as the Galois group of arithmetically profinite extensions of p-adic fields we answer affirmatively Coates--Greenberg's problem on deeply ramified extensions of local fields. Finally using the subgroup T we show that the wild group is not analytic over commutative complete local noetherian integral domains with finite residue field of characteristic p.

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