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Peer-reviewedCC BY 4.0Forum of Mathematics, Sigma

Perfect complexes and completion

  • Paul Balmer1
  • Beren Sanders2
  1. 1UCLA
  2. 2University of California
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Abstract

Let R ^ R̂ ModifyingAbove upper R With caret be the I -adic completion of a commutative ring R with respect to a finitely generated ideal I . We give a necessary and sufficient criterion for the category of perfect complexes over R ^ R̂ ModifyingAbove upper R With caret to be equivalent to the subcategory of dualizable objects in the derived category of I -complete complexes of R -modules. Our criterion is always satisfied when R is noetherian. When specialized to R local and noetherian and to I the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause, and Pevtsova.

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Cite

BibTeXRIS
BibTeX
@article{balmer2026perfect,
  title = {{Perfect complexes and completion}},
  author = {Paul Balmer and Beren Sanders},
  journal = {Forum of Mathematics, Sigma},
  year = {2026},
  month = oct,
  doi = {10.1017/fms.2026.10283},
  url = {https://www.cambridge.org/core/product/identifier/S2050509426102837/type/journal_article},
  note = {CC BY 4.0},
}
RIS
TY  - JOUR
TI  - Perfect complexes and completion
AU  - Paul Balmer
AU  - Beren Sanders
PY  - 2026
DA  - 2026/10/23
JO  - Forum of Mathematics, Sigma
DO  - 10.1017/fms.2026.10283
UR  - https://www.cambridge.org/core/product/identifier/S2050509426102837/type/journal_article
AB  - Let R ^ R̂_ ModifyingAbove upper R With caret be the I -adic completion of a commutative ring R with respect to a finitely generated ideal I . We give a necessary and sufficient criterion for the category of perfect complexes over R ^ R̂_ ModifyingAbove upper R With caret to be equivalent to the subcategory of dualizable objects in the derived category of I -complete complexes of R -modules. Our criterion is always satisfied when R is noetherian. When specialized to R local and noetherian and to I the maximal ideal, our theorem recovers a recent result of Benson, Iyengar, Krause, and Pevtsova.
SN  - 2050-5094
ER  -