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 |
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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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