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 <ibf@maths.nott.ac.uk>