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Title: | Noncommutative motives of Azumaya algebras | Authors: | Tabuada, Goncalo VAN DEN BERGH, Michel |
Issue Date: | 2015 | Publisher: | CAMBRIDGE UNIV PRESS | Source: | JOURNAL OF THE INSTITUTE OF MATHEMATICS OF JUSSIEU, 14 (2), p. 379-403 | 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. | Notes: | [Tabuada, Goncalo] MIT, Dept Math, Cambridge, MA 02139 USA. [Tabuada, Goncalo] FCT UNL, Dept Matemat, P-2829516 Caparica, Portugal. [Tabuada, Goncalo] FCT UNL, CMA, P-2829516 Caparica, Portugal. [van den Bergh, Michel] Univ Hasselt, Dept WNI, B-3590 Diepenbeek, Belgium. | Keywords: | algebraic K-theory; Azumaya algebras; cyclic homology; nilinvariance; noncommutative algebraic geometry; noncommutative motives;algebraic K-theory; Azumaya algebras; cyclic homology; nilinvariance; noncommutative algebraic geometry; noncommutative motives | Document URI: | http://hdl.handle.net/1942/18986 | ISSN: | 1474-7480 | e-ISSN: | 1475-3030 | DOI: | 10.1017/S147474801400005X | ISI #: | 000354708000003 | Rights: | © Cambridge University Press 2014 | Category: | A1 | Type: | Journal Contribution | Validations: | ecoom 2016 |
Appears in Collections: | Research publications |
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