Frobenius categories, Gorenstein algebras and rational surface singularities

Kalck, M., Iyama, O., Wemyss, M. and Yang, D. (2015) Frobenius categories, Gorenstein algebras and rational surface singularities. Compositio Mathematica, 151(3), pp. 502-534. (doi:10.1112/S0010437X14007647)

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Abstract

We give sufficient conditions for a Frobenius category to be equivalent to the category of Gorenstein projective modules over an Iwanaga–Gorenstein ring. We then apply this result to the Frobenius category of special Cohen–Macaulay modules over a rational surface singularity, where we show that the associated stable category is triangle equivalent to the singularity category of a certain discrepant partial resolution of the given rational singularity. In particular, this produces uncountably many Iwanaga–Gorenstein rings of finite Gorenstein projective type. We also apply our method to representation theory, obtaining Auslander–Solberg and Kong type results.

Item Type:Articles
Status:Published
Refereed:Yes
Glasgow Author(s) Enlighten ID:Wemyss, Professor Michael
Authors: Kalck, M., Iyama, O., Wemyss, M., and Yang, D.
College/School:College of Science and Engineering > School of Mathematics and Statistics > Mathematics
Journal Name:Compositio Mathematica
Publisher:Cambridge University Press
ISSN:0010-437X
ISSN (Online):1570-5846
Published Online:28 October 2015
Copyright Holders:Copyright © 2015 Cambridge University Press
First Published:First published in Compositio Mathematica 151(3):502-534
Publisher Policy:Reproduced in accordance with the copyright policy of the publisher

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