### Motives of Azumaya algebras, by Bruno Kahn and Marc Levine

[A revision was submitted November 3, 2009, with this comment:]

This is the final, revised version of preprint #875, to appear in the J.
Inst. Math. Jussieu.

[The original paper, submitted Oct 29, 2007, has been revised Feb 17, 2008,
with this comment:]

This is an update to #875. An error in prop. 4.6.1 and theorem 4.7.1 was
corrected by adding the hypothesis that A has square free index. Some
duplicate statements were consolidated and more detail on the use of the
Bloch-Kato conjectures was added.

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 SK_{2}(A) for a central simple algebra A of square-free index.

Bruno Kahn <kahn@math.jussieu.fr>

Marc Levine <marc@neu.edu>