Morita theory and singularity categories

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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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
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
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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