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Mat. Zametki, 1972, Volume 12, Issue 4, Pages 433–441 (Mi mz9902)  

Adams' operation and the symbol for the normed residue

V. L. Golo

M. V. Lomonosov Moscow State University

Abstract: 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.

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English version:
Mathematical Notes, 1972, 12:4, 693–698

Bibliographic databases:

UDC: 513.83
Received: 10.03.1971

Citation: V. L. Golo, “Adams' operation and the symbol for the normed residue”, Mat. Zametki, 12:4 (1972), 433–441; Math. Notes, 12:4 (1972), 693–698

Citation in format AMSBIB
\Bibitem{Gol72}
\by V.~L.~Golo
\paper Adams' operation and the symbol for the normed residue
\jour Mat. Zametki
\yr 1972
\vol 12
\issue 4
\pages 433--441
\mathnet{http://mi.mathnet.ru/mz9902}
\mathscinet{http://www.ams.org/mathscinet-getitem?mr=391090}
\zmath{https://zbmath.org/?q=an:0254.12007}
\transl
\jour Math. Notes
\yr 1972
\vol 12
\issue 4
\pages 693--698
\crossref{https://doi.org/10.1007/BF01093676}


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