Non-abelian local reciprocity law

Following our work on the generalized Fesenko reciprocity map, we construct the non-abelian local reciprocity map ${pmb{Phi}_K^{(varphi)}}$ of a local field K as a certain isomorphism from the absolute Galois group G _K of K onto a topological group ${nabla_{K,Y}^{(varphi)}}$ whose definition involves Fontaine–Wintenberger theory of field of norms, and build the non-abelian local class field theory over K in the sense of Fesenko and Koch.