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arxiv: 2507.10486 · v2 · submitted 2025-07-14 · 🧮 math.AC

Recognition: unknown

G-levels of perfect complexes

Andrew J. Soto Levins, Antonia Kekkou, Justin Lyle, Lars Winther Christensen, Zachary Nason

classification 🧮 math.AC
keywords complexesinjectivedimensionfinitelyformulag-levelsgeneratedgorenstein
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We prove that a commutative noetherian ring $R$ is Gorenstein of dimension at most $d$ if $d+1$ is an upper bound on the G-levels of perfect $R$-complexes. For $R$ local, we prove a formula for levels, with respect to injective or Gorenstein injective $R$-modules, of $R$-complexes with finitely generated homology; it mimics Bass' classic formula for injective dimension of finitely generated $R$-modules.

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  1. A characterization of Cohen-Macaulay rings in terms of levels of perfect complexes

    math.AC 2026-04 unverdicted novelty 6.0

    A commutative noetherian ring is Cohen-Macaulay precisely when the levels of all its perfect complexes are finite with respect to G_C(R) for any semidualizing module C.