We prove Weibel’s conjecture for twisted -theory when twisting by a smooth proper connective dg-algebra. Our main contribution is showing we can kill a negative twisted -theory class using a projective birational morphism (in the same twisted setting). We extend the vanishing result to relative twisted -theory of a smooth affine morphism and describe counterexamples to some similar extensions.
"Weibel's conjecture for twisted $K$-theory." Ann. K-Theory 5 (3) 621 - 637, 2020. https://doi.org/10.2140/akt.2020.5.621