K-theory of valuation rings

2018/10/29 by Kelly, Shane, Morrow, Matthew · 2 citations
#FOS: Mathematics #K-Theory and Homology (math.KT)

paper · doi:10.48550/arxiv.1810.12203

Abstract

We prove several results showing that the algebraic K-theory of valuation rings behave 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.

Cited by

• Log syntomic cohomology of truncated polynomials and coordinate axes
• A motivic approach to rational p-adic cohomologies

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• Algebraic series and valuation rings over nonclosed fields
• Regularity of semi-valuation rings and homotopy invariance of algebraic K-theory
• A valuation theorem for Noetherian rings
• Extensions of a valuation from K to K[x]
• Extension of valuations in characteristic one