The derived depth formula for modules of finite quasi‐projective dimension

Abstract Let be a commutative Noetherian local ring. We prove a variety of new formulas for modules of finite quasi‐projective or finite quasi‐injective dimension. These include the Derived Depth Formula, itself an extension of Auslander's famous depth formula, a variation of the Derived Depth Formula for width, an extended version of Ischebeck's Formula, and a Dependency formula in the vein of Jorgensen. Several special cases of our main results are new even under stronger assumptions on the vanishing of various complete intersection dimensions.