# 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} }

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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