School of Mathematical & Statistical Sciences Faculty Publications

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

Document Type

Article

Publication Date

9-1-2026

Abstract

Let (Formula presented.) 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.

Comments

© 2026 The Author(s). The publishing rights in this article are licensed to the London Mathematical Society under an exclusive licence.

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Publication Title

Bulletin of the London Mathematical Society

DOI

10.1112/blms.70491

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