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K-theory of valuation rings

Part of: (Co)homology theory Higher algebraic $K$-theory

Published online by Cambridge University Press:  20 May 2021

Shane Kelly  and
Matthew Morrow
Shane Kelly
Affiliation:
Department of Mathematics, Tokyo Institute of Technology, 2-12-1 Ookayama, Meguro-ku, Tokyo152-8551, Japanshanekelly@math.titech.ac.jp
Matthew Morrow
Affiliation:
CNRS & IMJ-PRG, SU – 4 place Jussieu, Case 247, 75252Paris, Francematthew.morrow@imj-prg.fr
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Abstract

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.

Keywords

K-theoryvaluation rings

MSC classification

Primary: 19D50: Computations of higher $K$-theory of rings
Secondary: 14F30: $p$-adic cohomology, crystalline cohomology
Type
Research Article
Information
Compositio Mathematica , Volume 157 , Issue 6 , June 2021 , pp. 1121 - 1142
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Copyright
© The Author(s) 2021

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