Generalized Fesenko reciprocity map

The paper is a natural continuation and generalization of the works of Fesenko and of the authors. Fesenko's theory is carried over to infinite APF Galois extensions $L$ over a local field $K$ with a finite residue-class field $\kappa_K$ of $q=p^f$ elements, satisfying $\pmb{\mu}_p(K^{\mathrm{sep}})\subset K$ and $K\subset L\subset K_{\varphi^d}$, where the residue-class degree $[\kappa_L:\kappa_K]$ is equal to $d$. More precisely, for such extensions $L/K$ and a fixed Lubin-Tate splitting $\varphi$ over $K$, a $1$-cocycle

$$\pmb{\Phi}_{L/K}^{(\varphi)}:\mathrm{Gal}(L/K)\rightarrow K^\times/N_{L_0/K}L_0^\times\times U_{\widetilde{\mathbb{X}}(L/K)}^\diamond/Y_{L/L_0},$$

where $L_0=L\cap K^{nr}$, is constructed, and its functorial and ramification-theoretic properties are studied. The case of $d=1$ recovers the theory of Fesenko.