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Width and amplitude inequalities over DG-rings

  • Luigi Ferraro
  • Zachary Nason
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Abstract

We study width over commutative noetherian local differential graded (DG) rings with bounded homology. We establish a derived width formula and prove amplitude inequalities for the derived completion of derived Hom and tensor products. As applications, we obtain Iversen's amplitude inequality and a criterion ensuring that regular sequences on a DG-module are regular on the DG-ring. These applications recover results for DG-modules with finitely generated homology and also hold for derived complete DG-modules. Finally, we characterize Cohen--Macaulay DG-rings by the existence of a bounded derived complete DG-module of finite injective dimension whose amplitude equals that of the DG-ring. This provides a version of Bass' conjecture for derived complete DG-modules.

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Cite

BibTeXRIS
BibTeX
@misc{ferraro2026width,
  title = {{Width and amplitude inequalities over DG-rings}},
  author = {Luigi Ferraro and Zachary Nason},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.37878},
  eprint = {2610.37878},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.37878},
}
RIS
TY  - UNPB
TI  - Width and amplitude inequalities over DG-rings
AU  - Luigi Ferraro
AU  - Zachary Nason
PY  - 2026
DA  - 2026/10/27
PB  - arXiv
DO  - 10.48550/arxiv.2610.37878
UR  - https://arxiv.org/abs/2610.37878
AB  - We study width over commutative noetherian local differential graded (DG) rings with bounded homology. We establish a derived width formula and prove amplitude inequalities for the derived completion of derived Hom and tensor products. As applications, we obtain Iversen's amplitude inequality and a criterion ensuring that regular sequences on a DG-module are regular on the DG-ring. These applications recover results for DG-modules with finitely generated homology and also hold for derived complete DG-modules. Finally, we characterize Cohen--Macaulay DG-rings by the existence of a bounded derived complete DG-module of finite injective dimension whose amplitude equals that of the DG-ring. This provides a version of Bass' conjecture for derived complete DG-modules.
ER  -