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

 

All tilting modules are of finite type


Authors: Silvana Bazzoni and Jan Stovícek
Journal: Proc. Amer. Math. Soc. 135 (2007), 3771-3781
MSC (2000): Primary 16D90, 16D30; Secondary 03E75, 16G99.
Published electronically: August 30, 2007
MathSciNet review: 2341926
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Abstract: We prove that any infinitely generated tilting module is of finite type, namely that its associated tilting class is the Ext-orthogonal of a set of modules possessing a projective resolution consisting of finitely generated projective modules.


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Additional Information

Silvana Bazzoni
Affiliation: Dipartimento di Matematica Pura e Applicata, Universitá di Padova, Via Trieste 63, 35121 Padova, Italy
Email: bazzoni@math.unipd.it

Jan Stovícek
Affiliation: Katedra algebry MFF UK, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email: stovicek@karlin.mff.cuni.cz

DOI: http://dx.doi.org/10.1090/S0002-9939-07-08911-3
PII: S 0002-9939(07)08911-3
Keywords: Tilting modules, cotorsion pairs.
Received by editor(s): October 1, 2005
Received by editor(s) in revised form: September 9, 2006
Published electronically: August 30, 2007
Additional Notes: The first author was supported by Università di Padova (Progetto di Ateneo CDPA048343 “Decomposition and tilting theory in modules, derived and cluster categories”).
The second author was supported by a grant of the Industrie Club Duesseldorf, GAČR 201/05/H005, and the research project MSM 0021620839.
Communicated by: Martin Lorenz
Article copyright: © Copyright 2007 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.