[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 SK2(A) for a central simple algebra A of square-free index.