On just infinite pro-p-groups and arithmetically profinite extensions of local fields
Abstract
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.
- Publication:
-
arXiv Mathematics e-prints
- Pub Date:
- February 1998
- DOI:
- 10.48550/arXiv.math/9802092
- arXiv:
- arXiv:math/9802092
- Bibcode:
- 1998math......2092F
- Keywords:
-
- Mathematics - Group Theory;
- Mathematics - Number Theory;
- 11S15;
- 20F99;
- 22E99
- E-Print:
- 15 pages, AMSTeX