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arXiv · 2610.31392

Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions

Luigi Ferraro
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Abstract

For every pair of integers $d,n\geq1$, we construct a commutative noetherian local-Cohen-Macaulay DG-ring $A$ such that $\dim H^0(A)=d$, $\mathrm{amp}(A)=n$, $\mathrm{fpd}(A)=d-n$, and $\mathrm{FPD}(A)=d$. 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.

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Luigi Ferraro. 2026-10-22. Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions. https://arxiv.org/abs/2610.31392

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