Abstract
Ifs is a central nonzerodivisor of a ringA, letB denote thes-adic completion ofA. By a theorem of Karoubi, there is a long exact sequence relating theK-theory ofA, B, A[s −1], andB[s −1]. This sequence was first exploited by Vorst in his thesis. We give two applications of the Karoubi sequence: (1) an example of a 2-dimensional normal domain withNK 0≠0, answering a question of Murthy, and (2) a complete computation ofK 2 of an (affine) seminormal curve over an algebraically closed field.
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Supported by NSF Grant MCS-79-03537
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Weibel, C.A. K-Theory and analytic isomorphisms. Invent Math 61, 177–197 (1980). https://doi.org/10.1007/BF01390120
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DOI: https://doi.org/10.1007/BF01390120