The \(\text{K}\)-theory of perfectoid rings
type: Item
instance of: scholarly article
title: The \(\text{K}\)-theory of perfectoid rings
author: Ben Antieau
author: Akhil Mathew
author: Matthew Morrow
published in: Documenta Mathematica
publication date: 2022-11-23T00:00:00Z
full work available at URL: https://arxiv.org/abs/2203.06472
review text: Summary: We establish various properties of the \(p\)-adic algebraic \(\text{K}\)-theory of smooth algebras over perfectoid rings living over perfectoid valuation rings. In particular, the \(p\)-adic \(\text{K}\)-theory of such rings is homotopy invariant, and coincides with the \(p\)-adic \(\text{K}\)-theory of the \(p\)-adic generic fibre in high degrees. In the case of smooth algebras over perfectoid valuation rings of mixed characteristic the latter isomorphism holds in all degrees and generalises a result of Nizioł.
Mathematics Subject Classification ID: 19D50
Mathematics Subject Classification ID: 14G45
zbMATH DE Number: 7622610
zbMATH Keywords: algebraic \(K\)-theory
zbMATH Keywords: perfectoid rings
MaRDI profile type: Publication
OpenAlex ID: W4320026737
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DOI: 10.25537/DM.2022V27.1923-1951
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description: scientific article; zbMATH DE number 7622610