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Please use this identifier to cite or link to this item: http://hdl.handle.net/1942/18986

Title: NONCOMMUTATIVE MOTIVES OF AZUMAYA ALGEBRAS
Authors: Tabuada, Goncalo
VAN DEN BERGH, Michel
Issue Date: 2015
Publisher: CAMBRIDGE UNIV PRESS
Citation: 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.
URI: http://hdl.handle.net/1942/18986
DOI: 10.1017/S147474801400005X
ISI #: 000354708000003
ISSN: 1474-7480
Category: A1
Type: Journal Contribution
Validation: ecoom, 2016
Appears in Collections: Research publications

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