Continuity of K-theory: An example in equal characteristics

Dundas, Bjørn

doi:10.1090/S0002-9939-98-04382-2

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.

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