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)

Abstract

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
• Status: Published
• Refereed: Yes
• 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
• Publisher: Elsevier
• ISSN: 0021-8693
• 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