We prove several results showing that the algebraic $K$-theory of valuation rings behaves as though such rings were regular Noetherian, in particular an analogue of the Geisser–Levine theorem. We also give some new proofs of known results concerning cdh descent of algebraic $K$-theory.

中文翻译：

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估值环的K理论

我们证明了一些结果，这些结果表明估值环的代数$ K $理论表现得像这样的环是正则Noetherian环，特别是Geisser-Levine定理的类似物。我们还给出了有关代数$ K $-理论的cdh下降的已知结果的一些新证据。