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Resumen de The Nottingham group and local class field theory

François Laubie, Olivier Moioli

  • 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.


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