Explicit higher local class field theory
نویسندگان
چکیده
Consider now an approach based on a generalization [F2] of Neukirch’s approach [N]. Below is a modified system of axioms of class formations (when applied to topological K -groups) which imposes weaker restrictions than the classical axioms (cf. section 11). (A1). There is a Ẑ-extension of F . In the case of higher local fields let F pur/F be the extension which corresponds to K sep 0 /K0: F pur = ∪(l,p)=1F (μl); the extension F pur is called the maximal purely unramified extension of F . Denote by FrobF the lifting of the Frobenius automorphisms of K 0 /K0 . Then Gal(F pur/F ) ≃ Ẑ, FrobF 7→ 1.
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