Geodesic
Adams' operation and the symbol for the normed residue
Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 433-441.

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We study the possibility of a meaningful extension of the ring of cohomologies of a point using algebraic extensions of local fields. It appears that complex $K$-theory is a good model problem for this. We prove that the effect of the Adams operation on the cohomologies of a point in extended $K$-theory coincides with the symbol for the local Artin reciprocity law. $K$-theories contained in a fixed $K$-theory with extended ring of cohomologies of a point are defined by higher branching groups. 
@article{MZM_1972_12_4_a10,
     author = {V. L. Golo},
     title = {Adams' operation and the symbol for the normed residue},
     journal = {Matemati\v{c}eskie zametki},
     pages = {433--441},
     publisher = {mathdoc},
     volume = {12},
     number = {4},
     year = {1972},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a10/}
}
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V. L. Golo. Adams' operation and the symbol for the normed residue. Matematičeskie zametki, Tome 12 (1972) no. 4, pp. 433-441. http://geodesic.mathdoc.fr/item/MZM_1972_12_4_a10/