Filtrations via tensor actions

Stevenson, G. (2018) Filtrations via tensor actions. International Mathematics Research Notices, 2018(8), pp. 2535-2558. (doi: 10.1093/imrn/rnw325)

Abstract

We extend the work of Balmer, associating filtrations of essentially small tensor triangulated categories to certain dimension functions, to the setting of actions of rigidly-compactly generated tensor triangulated categories on compactly generated triangulated categories. We show that the towers of triangles associated to such a filtration can be used to produce filtrations of Gorenstein injective quasi-coherent sheaves on Gorenstein schemes. This extends and gives a new proof of a result of Enochs and Huang. In the case of local complete intersections, a further refinement of this filtration is given and we comment on some special properties of the associated spectral sequence in this case.

• 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: International Mathematics Research Notices
• Publisher: Oxford University Press
• ISSN: 1073-7928
• ISSN (Online): 1687-0247
• Published Online: 11 January 2017
• Copyright Holders: Copyright © 2017 The Author
• First Published: First published in International Mathematics Research Notices 2018(8): 2535-2558
• Publisher Policy: Reproduced in accordance with the copyright policy of the publisher