is the following true (all algebras and modules are assumed to be finite dimensional): The finitistic dimension of an algebra is equal to the supremum of projective dimensions of tilting modules? It is true for Gorenstein algebras, since there D(A) is a tilting module.
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1$\begingroup$ It is also true if the category of modules with finite global dimension is contravariantly finite, in particular it is true for finite representation type. $\endgroup$– Dag Oskar MadsenCommented Jan 31, 2017 at 0:22
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$\begingroup$ Yes, I also found that in jstor.org/stable/3072902?seq=1#page_scan_tab_contents. $\endgroup$– MareCommented Jan 31, 2017 at 9:10
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