2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/154865We 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.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 addedK-Theory and HomologyAlgebraic Geometry19E15; 14C25text