Geodesic
On a~theorem of Hurewicz and $K$-theory of complete discrete valuation rings
Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 119-131.

Voir la notice de l'article provenant de la source Math-Net.Ru

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. 
@article{IM2_1987_29_1_a6,
     author = {I. A. Panin},
     title = {On a~theorem of {Hurewicz} and $K$-theory of complete discrete valuation rings},
     journal = {Izvestiya. Mathematics },
     pages = {119--131},
     publisher = {mathdoc},
     volume = {29},
     number = {1},
     year = {1987},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a6/}
}
TY  - JOUR
AU  - I. A. Panin
TI  - On a~theorem of Hurewicz and $K$-theory of complete discrete valuation rings
JO  - Izvestiya. Mathematics 
PY  - 1987
SP  - 119
EP  - 131
VL  - 29
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a6/
LA  - en
ID  - IM2_1987_29_1_a6
ER  - 
%0 Journal Article
%A I. A. Panin
%T On a~theorem of Hurewicz and $K$-theory of complete discrete valuation rings
%J Izvestiya. Mathematics 
%D 1987
%P 119-131
%V 29
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a6/
%G en
%F IM2_1987_29_1_a6
I. A. Panin. On a~theorem of Hurewicz and $K$-theory of complete discrete valuation rings. Izvestiya. Mathematics , Tome 29 (1987) no. 1, pp. 119-131. http://geodesic.mathdoc.fr/item/IM2_1987_29_1_a6/

[1] Artin M., Mazur B., Etale homotopy, Lect. Notes Math., 100, Springer-Verlag, 1969 | MR | Zbl

[2] Bousfield A. K., Kan D. M., Homotopy limits, completions and localizations, Lect. Notes Math., 304, Springer-Verlag, 1972 | MR | Zbl

[3] Browder W., “Algebraic $K$-theory with coefficient $\mathbf Z /p\mathbf Z$”, Geometric applications of homotopy theory (Proc. Conf., Evanston, 1977), Lecture Notes in Math., 657, Springer, Berlin, 1978, 40–85 | MR

[4] Eilenberg S., MacLane S., “On the groups $H(\pi,n)$. II. Methods of computation”, Ann. Math., 60 (1954), 49–139 | DOI | MR | Zbl

[5] Hilton P., Mislin G., Roitberg J., Localizations of Nilpotent Groups and Spaces, North-Holland Publishing Co., 1975 | MR | Zbl

[6] Lect. Notes Math., 269, 270, 305, 1972

[7] Neisendorfer J., “Primary homotopy theory”, Memoirs Amer. Math. Soc., 25:232 (1980), 1–67 | MR

[8] Peterson F. P., Generalized cohomology groups, Thesis., Princeton Univ., 1955

[9] Serre J.-P., “Groupes d'homotopie et classes de groupes abeliens”, Ann. Math., 58 (1953), 258–294 | DOI | MR | Zbl

[10] Sullivan D., Geometricheskaya topologiya, Mir, M., 1975 | MR | Zbl

[11] Suslin A., On the $K$-theory of local fields, Preprint LOMI, E–2–83 | MR

[12] Suslin A., Stabilization in algebraic $K$-theory, Preprint LOMI, E–2–80

[13] Quillen D., “Higher algebraic $K$-theory”, Lect. Notes Math., 341 (1972), 85–147 | DOI | MR