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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Continuity of K-theory:
An example in equal characteristics


Author: Bjørn Ian Dundas
Journal: Proc. Amer. Math. Soc. 126 (1998), 1287-1291
MSC (1991): Primary 11S70; Secondary 13J05, 19D45, 19D50
MathSciNet review: 1452802
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Abstract: If $k$ is a perfect field of characteristic $p>0$, we show that the Quillen K-groups $K_{i}(k[[t]])$ are uniquely $p$-divisible for $i=2,3$. In fact, the Milnor K-groups $K^{M}_{n}(k((t)))$ are uniquely $p$-divisible for all $n>1$. This implies that $K(A)\to {\operatornamewithlimits{holim}}_{\overleftarrow {n}} K(A/\mathfrak{m}^{n})$ is $4$-connected after profinite completion for $A$ a complete discrete valuation ring with perfect residue field.


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Additional Information

Bjørn Ian Dundas
Affiliation: Department of Mathematical Sciences, Section Gløshaugen, The Norwegian University of Science and Technology, N-7034 Trondheim, Norway
Email: dundas@math.ntnu.no

DOI: http://dx.doi.org/10.1090/S0002-9939-98-04382-2
PII: S 0002-9939(98)04382-2
Keywords: Continuity of K-theory, complete discrete valuation ring, ring of formal power series, Milnor K-theory
Received by editor(s): October 17, 1996
Additional Notes: The author was supported by the Danish research academy.
Communicated by: Thomas Goodwillie
Article copyright: © Copyright 1998 American Mathematical Society