G-levels of perfect complexes
Lars Winther Christensen, Antonia Kekkou, Justin Lyle, Zachary Nason, and Andrew J. Soto Levins
TL;DR
This paper characterizes Gorenstein rings via bounds on the G-levels of perfect complexes and provides a formula for levels of complexes with finitely generated homology, extending classical results.
Contribution
It establishes a new criterion for Gorenstein rings based on G-level bounds and derives a formula for levels of complexes with finitely generated homology.
Findings
A commutative noetherian ring is Gorenstein of dimension at most d if d+1 bounds the G-levels of perfect complexes.
Derived a formula for levels of complexes with finitely generated homology in local rings.
Extended Bass' formula to Gorenstein injective modules and complexes.
Abstract
We prove that a commutative noetherian ring is Gorenstein of dimension at most if is an upper bound on the G-levels of perfect -complexes. For local, we prove a formula for levels, with respect to injective or Gorenstein injective -modules, of -complexes with finitely generated homology; it mimics Bass' classic formula for injective dimension of finitely generated -modules.
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