On just infinite pro-p-groups and arithmetically profinite extensions of local fields, by Ivan Fesenko
This paper has now appeared in J. f\"ur die reine und angew. Math.
1999, 517, 61--80, and so the preprint has been removed.
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.
Ivan Fesenko <email@example.com>