Vol. 5, No. 3, 2020

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Weibel's conjecture for twisted $K$-theory

Joel Stapleton

Vol. 5 (2020), No. 3, 621–637

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.

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algebraic $K$-theory, Brauer groups, excision
Mathematical Subject Classification 2010
Primary: 16E20, 19D35
Secondary: 14F22, 16K50
Received: 4 February 2020
Revised: 2 April 2020
Accepted: 20 April 2020
Published: 28 July 2020
Joel Stapleton
Joel Stapleton
University of Illinois at Chicago
Chicago, IL
United States