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arXiv · 2605.07004

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

Luigi Ferraro·Justin Lyle
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Abstract

Let $R$ be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Derived Depth Formula, itself an extension of Auslander 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.

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Luigi Ferraro, Justin Lyle. 2026-05-07. The derived depth formula for modules of finite quasi-projective dimension. https://arxiv.org/abs/2605.07004

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