Motives of Azumaya algebras

2007/10/08 by Bruno Kahn, Kahn, Bruno, Marc Levine +1 · 2 citations
Mathematics · #14C25 #19E15 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Algebraic structures and combinatorial models #FOS: Mathematics #K-Theory and Homology (math.KT)

paper · pdf · doi:10.48550/arxiv.0710.1614

openalex publication_date 2007/10/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

Cited by

• K(1)-local K-theory of Azumaya algebras
• Localizing motives of Azumaya algebras

Related

• K-theory of Azumaya algebras over schemes
• Virtual representation motives
• Noncommutative motives of separable algebras
• Abelian motives and Shimura varieties in nonzero characteristic
• Maximal orders in unramified central simple algebras