Tilting theory and the finitistic dimension conjectures

@article{AngeleriHugel2002TiltingTA,
title={Tilting theory and the finitistic dimension conjectures},
author={Lidia Angeleri-Hugel and Jan Trlifaj},
journal={Transactions of the American Mathematical Society},
year={2002},
volume={354},
pages={4345-4358}
}
• Published 24 June 2002
• Mathematics
• Transactions of the American Mathematical Society
Let R be a right noetherian ring and let P<∞ be the class of all finitely presented modules of finite projective dimension. We prove that findimR = n < ∞ iff there is an (infinitely generated) tilting module T such that pdT = n and T⊥ = (p<∞)⊥. If R is an artin algebra, then T can be taken to be finitely generated iff p<∞ is contravariantly finite. We also obtain a sufficient condition for validity of the First Finitistic Dimension Conjecture that extends the well-known result of Huisgen…
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