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 Mat. Zametki: Year: Volume: Issue: Page: Find

 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.

Full text: PDF file (887 kB)

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

Bibliographic databases:

UDC: 513.83

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}