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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Classifying Serre subcategories of finitely presented modules


Authors: Grigory Garkusha and Mike Prest
Journal: Proc. Amer. Math. Soc. 136 (2008), 761-770
MSC (2000): Primary 13C05, 13C11, 18E30, 18G35
Published electronically: November 30, 2007
MathSciNet review: 2361847
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Abstract: Given a commutative coherent ring $ R$, a bijective correspondence between the thick subcategories of perfect complexes $ \mathcal D_{{per}}(R)$ and the Serre subcategories of finitely presented modules is established. To construct this correspondence, properties of the Ziegler and Zariski topologies on the set of isomorphism classes of indecomposable injective modules are used in an essential way.


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Additional Information

Grigory Garkusha
Affiliation: Department of Mathematics, Swansea University, SA2 8PP Swansea, United Kingdom
Email: G.Garkusha@swansea.ac.uk

Mike Prest
Affiliation: Department of Mathematics, University of Manchester, Oxford Road, M13 9PL Manchester, United Kingdom
Email: mprest@maths.man.ac.uk

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08844-2
PII: S 0002-9939(07)08844-2
Keywords: Thick subcategories, perfect complexes, Ziegler and Zariski spectra
Received by editor(s): May 23, 2006
Received by editor(s) in revised form: July 5, 2006
Published electronically: November 30, 2007
Additional Notes: This paper was written during the visit of the first author to the University of Manchester, which was supported by the MODNET Research Training Network in Model Theory. He would like to thank the University for its kind hospitality.
Communicated by: Paul Goerss
Article copyright: © Copyright 2007 American Mathematical Society