The Nottingham group and local class field theory
- Autores: François Laubie, Olivier Moioli
- Localización: Journal of the London Mathematical Society, ISSN 0024-6107, Vol. 80, Nº 1, 2009, págs. 191-211
- Idioma: inglés
- DOI: 10.1112/jlms/jdp022
- Enlaces
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Resumen
Let Fq be the algebraic closure of the finite field Fq. Let G be the group of continuous Fq-automorphisms �Ð of the abelian closure of the series field Fq((t)) such that �Ð(t) �¸ tFq[[t]] �~ .
The set Fq[[t]] �~ is a group for the non-commutative Ore multiplication of the series (the ordinary multiplication twisted by the Frobenius map). In this paper, by means of the Koch.de Shalit reciprocity map, we construct a subgroup W of this group and an isomorphism �Ç of W onto G, which extends the Artin reciprocity map. Thus the Nottingham group can be described with Ore multiplication; this description gives rise to a larger interpretation of the Schmid local symbol and gives some information on its finite abelian subgroups. We study the behaviour of �Ç relative to ramification and norm mapping.
