All tilting modules are of finite type
Authors:
Silvana Bazzoni and Jan Šťovíček
Journal:
Proc. Amer. Math. Soc. 135 (2007), 3771-3781
MSC (2000):
Primary 16D90, 16D30; Secondary 03E75, 16G99.
DOI:
https://doi.org/10.1090/S0002-9939-07-08911-3
Published electronically:
August 30, 2007
MathSciNet review:
2341926
Full-text PDF Free Access
Abstract | References | Similar Articles | Additional Information
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
MR Author ID:
33015
Email:
bazzoni@math.unipd.it
Jan Šťovíček
Affiliation:
Katedra algebry MFF UK, Sokolovská 83, 186 75 Praha 8, Czech Republic
Email:
stovicek@karlin.mff.cuni.cz
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.
