Motives of Azumaya algebras

Abstract

AbstractWe study the slice filtration for theK-theory of a sheaf of Azumaya algebrasA, 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 ofSK2(A) for a central simple algebraAof square-free index (prime to the characteristic). This proves a conjecture of Merkurjev.