On the vanishing of Twisted negative K-theory and homotopy invariance

TL;DR

This paper investigates the behavior of twisted negative K-theory, confirming vanishing results for certain domains and establishing homotopy invariance in specific algebraic contexts.

Contribution

It provides new insights into Weibel's conjecture for twisted K-theory and proves homotopy invariance for Pr"ufer domains.

Findings

Vanishing of twisted negative K-groups for Pr"ufer domains

Homotopy invariance of twisted K-theory for finite-dimensional Pr"ufer domains

Confirmation of Weibel's conjecture in the twisted setting

Abstract

In this article, we revisit Weibel's conjecture for twisted $K$-theory. We also examine the vanishing of twisted negative $K$-groups for Pr\"{u}fer domains. Furthermore, we observe that the homotopy invariance of twisted $K$-theory holds for (finite-dimensional) Pr\"{u}fer domains.