2008/05/22 by Kâzım İlhan İkeda, Ikeda, Kâzim İlhan, Erol Serbest +1
Mathematics · #11S37 #Advanced Algebra and Geometry #Algebraic Geometry and Number Theory #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.0805.3431
openalex publication_date 2008/05/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, which is the natural continuation and generalization of Fesenko's non-abelian reciprocity map, we extend the theory of Fesenko to infinite APF-Galois extensions L over a local field K, with finite residue-class field κK of q=pf elements, satisfying \pmbμp(Ksep)⊂ K and K⊂ L⊂ Kϕd where the residue-class degree [κL:κK]=d. More precisely, for such extensions L/K, fixing a Lubin-Tate splitting ϕ over K, we construct a 1-cocycle, \pmbΦL/K(ϕ):Gal(L/K)→ K^×/NL0/KL0^×× U_\widetilde\mathbb X(L/K)^\diamond /YL/L0, where L0=L∩ Knr, and study its functorial and ramification-theoretic properties. The case d=1 recovers the theory of Fesenko.