K-theory of valuation rings

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.

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Bibliographic Details
Published inCompositio mathematica Vol. 157; no. 6; pp. 1121 - 1142
Main Authors Kelly, Shane, Morrow, Matthew
Format Journal Article
LanguageEnglish
Published London, UK London Mathematical Society 01.06.2021
Cambridge University Press
Foundation Compositio Mathematica
Subjects
Algebra
K-Theory and Homology
Mathematics
Rings (mathematics)
Valuation
19D50
valuation rings
14F30
K-theory
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Summary: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.
ISSN:0010-437X
1570-5846
DOI:10.1112/S0010437X21007119