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K-theory of admissible Zariski–Riemann spaces

Christian Dahlhausen

Vol. 8 (2023), No. 1, 1–23
Abstract

We study relative algebraic K-theory of admissible Zariski–Riemann spaces and prove that it is equivalent to relative G-theory and satisfies homotopy invariance. Moreover, we provide an example of a nonnoetherian abelian category whose negative K-theory vanishes.

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Keywords
K-theory, Zariski–Riemann spaces
Mathematical Subject Classification
Primary: 19D35, 19E08
Milestones
Received: 26 March 2021
Revised: 12 January 2023
Accepted: 30 January 2023
Published: 1 May 2023
Authors
Christian Dahlhausen
Mathematisches Institut
Universität Heidelberg
Heidelberg
Germany