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severi–brauer schemes

Journal of the Institute of Mathematics of Jussieu (1)

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1 results

Motives of Azumaya algebras
Part of
- $K$-theory in geometry
- Cycles and subschemes
Bruno Kahn, Marc Levine
Journal:

Journal of the Institute of Mathematics of Jussieu / Volume 9 / Issue 3 / July 2010

Published online by Cambridge University Press:

14 April 2010, pp. 481-599

Print publication:

July 2010
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We study the slice filtration for the K-theory of a sheaf of Azumaya algebras A, and for the motive of a Severi-Brauer variety, the latter in the case of a central simple algebra of prime degree over a field. Using the Beilinson–Lichtenbaum conjecture, we apply our results to show the vanishing of SK2(A) for a central simple algebra A of square-free index (prime to the characteristic). This proves a conjecture of Merkurjev.