Noncommutative motives of Azumaya algebras

Gonçalo Jorge Trigo Neri Tabuada, Michel van den Bergh

Research output: Contribution to journalArticle

17 Citations (Scopus)

Abstract

Let k be a base commutative ring, R a commutative ring of coefficients, X a quasi-compact quasi-separated k-scheme, and A a sheaf of Azumaya algebras over X of rank r. Under the assumption that 1/r is an element of R, we prove that the noncommutative motives with R-coefficients of X and A are isomorphic. As an application, we conclude that a similar isomorphism holds for every R-linear additive invariant. This leads to several computations. Along the way we show that, in the case of finite-dimensional algebras of finite global dimension, all additive invariants are nilinvariant.
Original languageEnglish
Pages (from-to)379-403
JournalJournal of the Institute of Mathematics of Jussieu
Volume14
Issue number2
DOIs
Publication statusPublished - Apr 2015

Keywords

  • algebraic K-theory
  • Azumaya algebras
  • cyclic homology
  • nilinvariance
  • noncommutative algebraic geometry
  • noncommutative motives

Fingerprint Dive into the research topics of 'Noncommutative motives of Azumaya algebras'. Together they form a unique fingerprint.

Cite this