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 Izv. Akad. Nauk SSSR Ser. Mat., 1986, Volume 50, Issue 4, Pages 763–775 (Mi izv1532)

On a theorem of Hurewicz and $K$-theory of complete discrete valuation rings

I. A. Panin

Abstract: It is proved that for a complete discrete valuation ring $\mathfrak D$ of zero characteristic with residue field $k$ of positive characteristic $p$ and maximal ideal $\mathfrak M$, the natural homomorphism of $K$-groups with coefficients
$$K_i(\mathfrak D;\mathbf Z/p^n\mathbf Z)\to\varprojlim_iK_i(\mathfrak D/\mathfrak M^j;\mathbf Z/p^n\mathbf Z)$$
is an isomorphism for all positive $i$ and $n$.
For the ring of integers $\mathfrak D$ in a local field $K/\mathbf Q_p$, the groups $K_i(\mathfrak D;\mathbf Z/p^n\mathbf Z)$ are finite.
Bibliography: 13 titles.

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English version:
Mathematics of the USSR-Izvestiya, 1987, 29:1, 119–131

Bibliographic databases:

UDC: 513.6
MSC: 18F25, 13F30

Citation: I. A. Panin, “On a theorem of Hurewicz and $K$-theory of complete discrete valuation rings”, Izv. Akad. Nauk SSSR Ser. Mat., 50:4 (1986), 763–775; Math. USSR-Izv., 29:1 (1987), 119–131

Citation in format AMSBIB
\Bibitem{Pan86} \by I.~A.~Panin \paper On a~theorem of Hurewicz and $K$-theory of complete discrete valuation rings \jour Izv. Akad. Nauk SSSR Ser. Mat. \yr 1986 \vol 50 \issue 4 \pages 763--775 \mathnet{http://mi.mathnet.ru/izv1532} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=864175} \zmath{https://zbmath.org/?q=an:0622.18006|0614.18009} \transl \jour Math. USSR-Izv. \yr 1987 \vol 29 \issue 1 \pages 119--131 \crossref{https://doi.org/10.1070/IM1987v029n01ABEH000962} 

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Citing articles on Google Scholar: Russian citations, English citations
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This publication is cited in the following articles:
1. Lars Hesselholt, Ib Madsen, “On the K-theory of finite algebras over witt vectors of perfect fields”, Topology, 36:1 (1997), 29
2. Thomas Geisser, Lars Hesselholt, “Bi-relative algebraic K-theory and topological cyclic homology”, Invent math, 166:2 (2006), 359
3. Caroline Junkins, Manfred Kolster, “The analogue of the Gauss class number problem in motivic cohomology”, Ann. Math. Québec, 2013
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