9 citations · 18 across the 18 of their papers we have counts for
21 papers
Local-Cohen-Macaulay DG-rings with unequal finitistic projective dimensions
Luigi Ferraro
For every pair of integers , we construct a commutative noetherian local-Cohen-Macaulay DG-ring such that , , ,…
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…
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…
The derived depth formula for modules of finite quasi-projective dimension
Luigi Ferraro, Justin Lyle
Let 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…
Trimming Five Generated Gorenstein Ideals
Luigi Ferraro, W. Frank Moore
Let be a regular local ring of dimension 3. Let be a Gorenstein ideal of of grade 3. It follows from a result of Buchsbaum and Eisenbud that there…
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…
The Tor algebra of trimmings of Gorenstein ideals
Luigi Ferraro, Alexis Hardesty
Let be a regular local ring of dimension 3. Let be a Gorenstein ideal of of grade 3. Buchsbaum and Eisenbud proved that there is a skew-symmetric m…
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…
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 and their relation to the canonical projection , where …
The Taylor resolution over a skew polynomial ring
Luigi Ferraro, Desiree Martin, W. Frank Moore
Let be a field and let be a monomial ideal in the polynomial ring . In her thesis, Taylor introduced a complex which provides a finite free res…
The Eliahou-Kervaire resolution over a skew polynomial ring
Luigi Ferraro, Alexis Hardesty
In a 1987 paper, Eliahou and Kervaire constructed a minimal resolution of a class of monomial ideals in a polynomial ring, called stable ideals. As a consequence of their construct…
Support varieties over skew complete intersections via derived braided Hochschild cohomology
Luigi Ferraro, W. Frank Moore, Josh Pollitz
In this article we study a theory of support varieties over a skew complete intersection , i.e. a skew polynomial ring modulo an ideal generated by a sequence of regular normal…
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…
On the Noether Bound for Noncommutative Rings
Luigi Ferraro, Ellen Kirkman, W. Frank Moore +1
We present two noncommutative algebras over a field of characteristic zero that each posses a family of actions by cyclic groups of order , represented in matrices…
Semisimple Reflection Hopf Algebras of Dimension Sixteen
Luigi Ferraro, Ellen Kirkman, W. Frank Moore +1
For each nontrivial semisimple Hopf algebra of dimension sixteen over , the smallest dimension inner-faithful representation of acting on a quadratic AS regular…
Simple -graded domains of Gelfand-Kirillov dimension two
Luigi Ferraro, Jason Gaddis, Robert Won
Let be an algebraically closed field and a -graded finitely generated simple -algebra which is a domain of Gelfand-Kirillov dimension 2. We show that the cat…
Differential graded algebra over quotients of skew polynomial rings by normal elements
Luigi Ferraro, W. Frank Moore
Differential graded algebra techniques have played a crucial role in the development of homological algebra, especially in the study of homological properties of commutative rings…
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 with residue field , stable cohomo…
Three infinite families of reflection Hopf algebras
Luigi Ferraro, Ellen Kirkman, W. Frank Moore +1
Let be a semisimple Hopf algebra acting on an Artin-Schelter regular algebra , homogeneously, inner-faithfully, preserving the grading on , and so that is an -modu…
Modules of infinite regularity over commutative graded rings
Luigi Ferraro
In this work, we prove that if a graded, commutative algebra over a field is not Koszul then, denoting by the maximal homogeneous ideal of and by a f…
Regularity of Tor for weakly stable ideals
Katie Ansaldi, Nicholas Clarke, Luigi Ferraro
It is proved that if and are weakly stable ideals in a polynomial ring , with a field, then the regularity of has the exp…