<i>K</i>-theory of valuation rings

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Abstract

<jats:p>We prove several results showing that the algebraic<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0010437X21007119_inline2.png" /><jats:tex-math>$K$</jats:tex-math></jats:alternatives></jats:inline-formula>-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<jats:inline-formula><jats:alternatives><jats:inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" mime-subtype="png" xlink:href="S0010437X21007119_inline3.png" /><jats:tex-math>$K$</jats:tex-math></jats:alternatives></jats:inline-formula>-theory.</jats:p>

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