Abstract

We prove Weibel’s conjecture for twisted $K$-theory when twisting by a smooth proper connective dg-algebra. Our main contribution is showing we can kill a negative twisted $K$-theory class using a projective birational morphism (in the same twisted setting). We extend the vanishing result to relative twisted $K$-theory of a smooth affine morphism and describe counterexamples to some similar extensions.

Keywords

Mathematical Subject Classification 2010

Milestones

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