The local-to-global principle for triangulated categories via dimension functions

Stevenson, G. (2017) The local-to-global principle for triangulated categories via dimension functions. Journal of Algebra, 473, pp. 406-429. (doi: 10.1016/j.jalgebra.2016.12.002)

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We formulate a general abstract criterion for verifying the local-to-global principle for a rigidly-compactly generated tensor triangulated category. Our approach is based upon an inductive construction using dimension functions. Using our criterion we give a new proof of the theorem that the local-to-global principle holds for such categories when they have a model and the spectrum of the compacts is noetherian. As further applications we give a new set of conditions on the spectrum of the compacts that guarantee the local-to-global principle holds and use this to classify localising subcategories in the derived category of a semi-artinian absolutely flat ring.

Item Type:Articles
Glasgow Author(s) Enlighten ID:Stevenson, Dr Gregory
Authors: Stevenson, G.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Journal of Algebra
ISSN (Online):1090-266X
Published Online:07 December 2016
Copyright Holders:Copyright © 2016 Elsevier Inc.
First Published:First published in Journal of Algebra 473:406-429
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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