Weibel's conjecture for twisted K-theory

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 counter examples to some similar extensions.

arXiv commentfinal version, 14 pages, comments welcome

References in corpus (3)

• Brauer groups and étale cohomology in derived algebraic geometry
• Algebraic K-theory and descent for blow-ups
• On the K-theory of pullbacks

Cited by in corpus (1)

• Categorical Milnor squares and K-theory of algebraic stacks