Luigi Ferraro

activity

20152026

most citedThree infinite families of reflection Hopf algebras

9 citations · 18 across the 18 of their papers we have counts for

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13 papers · 1 filter

math.AC2026

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

Luigi Ferraro

For every pair of integers $d, n \geq 1$ , we construct a commutative noetherian local-Cohen-Macaulay DG-ring $A$ such that $dim H^{0} (A) = d$ , $amp (A) = n$ , $fpd (A) = d - n$ ,…

math.AC2026

Intersection theorems over DG-rings revisited

Luigi Ferraro, Zachary Nason

In this work we generalize two recently proved intersection theorems for DG-rings. The Derived Improved New Intersection Theorem concerns the length of semi-free DG-modules over DG…

math.AC2026

Amplitude inequalities for local (co)homology

Lars Winther Christensen, Luigi Ferraro, Henrik Holm

Peskine and Szpiro's Intersection Theorem for finitely generated modules was generalized by Foxby to all modules and bounded complexes of such. We strengthen Foxby's result and pro…

math.AC2026

The derived depth formula for modules of finite quasi-projective dimension

Luigi Ferraro, Justin Lyle

Let $R$ be a commutative Noetherian local ring. We prove a variety of new formulae for modules of finite quasi-projective or finite quasi-injective dimension. These include the Der…

math.AC2024

Trimming Five Generated Gorenstein Ideals

Luigi Ferraro, W. Frank Moore

Let $(R, m, k)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. It follows from a result of Buchsbaum and Eisenbud that there…

math.AC2022

The Improved New Intersection Theorem revisited

Lars Winther Christensen, Luigi Ferraro

We prove a generalized version of Evans and Griffith's Improved New Intersection Theorem: Let I be an ideal in a local ring R. If a finite free R-complex, concentrated in nonnegati…

math.AC2022

The Tor algebra of trimmings of Gorenstein ideals

Luigi Ferraro, Alexis Hardesty

Let $(R, m, k)$ be a regular local ring of dimension 3. Let $I$ be a Gorenstein ideal of $R$ of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric m…

math.AC2021

Rigidity of Ext and Tor via flat-cotorsion theory

Lars Winther Christensen, Luigi Ferraro, Peder Thompson

Let p be a prime ideal in a commutative noetherian ring R and denote by k(p) the residue field of the local ring R_p. We prove that if an R-module M satisfies Ext_R^n(k(p),M) = 0 f…

math.AC2021

The homotopy Lie algebra of a Tor-independent tensor product

Luigi Ferraro, Mohsen Gheibi, David A. Jorgensen +2

In this article we investigate a pair of surjective local ring maps $S_{1} \leftarrow R \to S_{2}$ and their relation to the canonical projection $R \to S_{1} \otimes_{R} S_{2}$ , where $S_{1}, S_{2}$ …

math.AC2020★ 2 cited

The InvariantRing package for Macaulay2

Luigi Ferraro, Federico Galetto, Francesca Gandini +3

We describe a significant update to the existing InvariantRing package for Macaulay2. In addition to expanding and improving the methods of the existing package for actions of fini…

math.AC2018

A bimodule structure for the bounded cohomology of commutative local rings

Luigi Ferraro

Stable cohomology is a generalization of Tate cohomology to associative rings, first defined by Pierre Vogel. For a commutative local ring $R$ with residue field $k$ , stable cohomo…

math.AC2018

Modules of infinite regularity over commutative graded rings

Luigi Ferraro

In this work, we prove that if a graded, commutative algebra $R$ over a field $k$ is not Koszul then, denoting by $m$ the maximal homogeneous ideal of $R$ and by $M$ a f…

math.AC2015

Regularity of Tor for weakly stable ideals

Katie Ansaldi, Nicholas Clarke, Luigi Ferraro

It is proved that if $I$ and $J$ are weakly stable ideals in a polynomial ring $R = k [x_{1}, \dots, x_{n}]$ , with $k$ a field, then the regularity of $Tor_{i}^{R} (R / I, R / J)$ has the exp…