Greenlees, J.P.C. and Stevenson, G. (2020) Morita theory and singularity categories. Advances in Mathematics, 365, 107055. (doi: 10.1016/j.aim.2020.107055)
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Abstract
We propose an analogue of the bounded derived category for an augmented ring spectrum, defined in terms of a notion of Noether normalization. In many cases we show this category is independent of the chosen normalization. Based on this, we define the singularity and cosingularity categories measuring the failure of regularity and coregularity and prove they are Koszul dual in the style of the BGG correspondence. Examples of interest include Koszul algebras and Ginzburg DG-algebras, C⁎ (BG) for finite groups (or for compact Lie groups with orientable adjoint representation), cochains in rational homotopy theory and various examples from chromatic homotopy theory.
Item Type: | Articles |
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Status: | Published |
Refereed: | Yes |
Glasgow Author(s) Enlighten ID: | Stevenson, Dr Gregory |
Authors: | Greenlees, J.P.C., and Stevenson, G. |
College/School: | College of Science and Engineering > School of Mathematics and Statistics > Mathematics |
Journal Name: | Advances in Mathematics |
Publisher: | Elsevier |
ISSN: | 0001-8708 |
ISSN (Online): | 1090-2082 |
Published Online: | 18 February 2020 |
Copyright Holders: | Copyright © 2020 Elsevier Inc. |
First Published: | First published in Advances in Mathematics 365:107055 |
Publisher Policy: | Reproduced in accordance with the publisher copyright policy |
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