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Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions
Abstract
For every pair of integers d,n≥1, we construct a commutative noetherian local-Cohen-Macaulay DG-ring A such that dim H0(A)=d, amp(A)=n, fpd(A)=d−n, and FPD(A)=d. This gives a negative answer to the implication from local-Cohen-Macaulayness to equality of the two finitistic projective dimensions in a question of Bird, Shaul, Sridhar, and Williamson.
Related
- Finitistic injective dimension exceeding finitistic projective dimension for a commutative ring
- Derived Delooping Levels of One-Point Extensions and Finitistic Dimensions
- Bounds on Hilbert coefficients of Cohen-Macaulay modules having finite projective dimension
- Sharp effective Nullstellensatz for projective Cohen-Macaulay schemes
- The finitistic weak dimensions of Gaussian rings
BibTeX
@misc{ferraro2026localcohenmacaulay,
title = {{Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions}},
author = {Luigi Ferraro},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.31392},
eprint = {2610.31392},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.31392},
}
RIS
TY - UNPB
TI - Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions
AU - Luigi Ferraro
PY - 2026
DA - 2026/10/22
PB - arXiv
DO - 10.48550/arxiv.2610.31392
UR - https://arxiv.org/abs/2610.31392
AB - For every pair of integers d,n≥1, we construct a commutative noetherian local-Cohen-Macaulay DG-ring A such that dim H^0(A)=d, amp(A)=n, fpd(A)=d−n, and FPD(A)=d. This gives a negative answer to the implication from local-Cohen-Macaulayness to equality of the two finitistic projective dimensions in a question of Bird, Shaul, Sridhar, and Williamson.
ER -