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)

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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
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 (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

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