Tilting theory and the finitistic dimension conjectures

Let R be a right noetherian ring and let Plt;∞ 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-Zimmermann and Smalø.