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

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.