## Continuity of K-theory: An example in equal characteristics

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- by Bjørn Ian Dundas
- Proc. Amer. Math. Soc.
**126**(1998), 1287-1291 - DOI: https://doi.org/10.1090/S0002-9939-98-04382-2
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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 $K(A)\to {\operatorname *{holim}}_{\overleftarrow {n}} K(A/\mathfrak {m}^{n})$ is $4$-connected after profinite completion for $A$ a complete discrete valuation ring with perfect residue field.## References

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## Bibliographic 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
- Received by editor(s): October 17, 1996
- Additional Notes: The author was supported by the Danish research academy.
- Communicated by: Thomas Goodwillie
- © Copyright 1998 American Mathematical Society
- Journal: Proc. Amer. Math. Soc.
**126**(1998), 1287-1291 - MSC (1991): Primary 11S70; Secondary 13J05, 19D45, 19D50
- DOI: https://doi.org/10.1090/S0002-9939-98-04382-2
- MathSciNet review: 1452802