Volume 22, issue 1 (2022)

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On the algebraic $K$–theory of double points

Noah Riggenbach

Algebraic & Geometric Topology 22 (2022) 373–403
Abstract

We use trace methods to study the algebraic K–theory of rings of the form R[x1,,xd](x1,,xd)2. We compute the relative p–adic K groups for R a perfectoid ring. In particular, we get the integral K groups when R is a finite field, and the integral relative K groups K(R[x1,,xd](x1,,xd)2,(x1,,xd)) when R is a perfect 𝔽p–algebra. We conclude with some other notable computations, including some rings which are not quite of the above form.

Keywords
K–theory, topological cyclic homology, perfectoid ring, K–theory of singular schemes
Mathematical Subject Classification
Primary: 19D50
Secondary: 14G45, 19D55, 55P42, 55P91
References
Publication
Received: 7 August 2020
Revised: 11 January 2021
Accepted: 12 February 2021
Published: 26 April 2022
Authors
Noah Riggenbach
Department of Mathematics
Indiana University
Bloomington, IN
United States
Department of Mathematics
Northwestern University
Evanston, IL
United States