28 citations · 194 across the 25 of their papers we have counts for
29 papers
K-injective complexes in commutative algebra
Liran Shaul
It is an unfortunate fact that even over commutative noetherian rings, localization of K-injective complexes need not be K-injective. However, not all is lost. Given a complex of i…
Formalization in Lean of faithfully flat descent of projectivity
Liran Shaul
We formalize in Lean the following foundational result in commutative algebra: Let be a faithfully flat map of (not necessarily noetherian) commutative rings, and let …
Openness with respect to levels in triangulated categories
Souvik Dey, Jian Liu, Liran Shaul
Given a compactly generated triangulated category equipped with an action of a graded-commutative Noetherian ring , generalizing results of Letz, we prove a genera…
Gorenstein acyclic complexes and finitistic dimensions
Liran Shaul
Given a two-sided noetherian ring with a dualizing complex, we show that the big finitistic dimension of is finite if and only if every bounded below Gorenstein-projective-…
Acyclic complexes of injectives and finitistic dimensions
Liran Shaul
For a ring , we consider the question whether every bounded above cochain complex of injective -modules which is acyclic is null-homotopic. We show that if is left and ri…
Categorical properties of reduction functors over non-positive DG-rings
Liran Shaul
Given a non-positive DG-ring , associated to it are the reduction and coreduction functors and $G(-) = \mathrm{R}\operatorname{H…
The finitistic dimension conjecture via DG-rings
Liran Shaul
Given an associative ring , we present a new approach for establishing the finiteness of the big finitistic projective dimension . The idea is to find a s…
Finitistic dimensions over commutative DG-rings
Isaac Bird, Liran Shaul, Prashanth Sridhar +1
In this paper we study the finitistic dimensions of commutative noetherian non-positive DG-rings with finite amplitude. We prove that any DG-module of finite flat dimension ove…
Sequence-regular commutative DG-rings
Liran Shaul
We introduce a new class of commutative noetherian DG-rings which generalizes the class of regular local rings. These are defined to be local DG-rings such…
Lifting (co)stratifications between tensor triangulated categories
Liran Shaul, Jordan Williamson
We give necessary and sufficient conditions for stratification and costratification to descend along a coproduct preserving, tensor-exact -linear functor between -linear tens…
Smooth flat maps over commutative DG-rings
Liran Shaul
We study smooth maps that arise in derived algebraic geometry. Given a map between non-positive commutative noetherian DG-rings which is of flat dimension , we show th…
Koszul complexes over Cohen-Macaulay rings
Liran Shaul
We prove a Cohen-Macaulay version of a result by Avramov-Golod and Frankild-Jørgensen about Gorenstein rings, showing that if a noetherian ring is Cohen-Macaulay, and $a_1,\dot…
Open loci results for commutative DG-rings
Liran Shaul
Given a commutative noetherian non-positive DG-ring with bounded cohomology which has a dualizing DG-module, we study its regular, Gorenstein and Cohen-Macaulay loci. We give a suf…
The Cohen-Macaulay property in derived commutative algebra
Liran Shaul
By extending some basic results of Grothendieck and Foxby about local cohomology to commutative DG-rings, we prove new amplitude inequalities about finite DG-modules of finite inje…
Pole placement for overdetermined 2D systems
Liran Shaul, Victor Vinnikov
We formulate and solve a pole placement problem by state feedback for overdetermined 2D systems modeled by commutative operator vessels. In this setting, the transfer function of t…
Injective DG-modules over non-positive DG-rings
Liran Shaul
Let be an associative non-positive differential graded ring. In this paper we make a detailed study of a category of left DG-modules over w…
Homological dimensions of local (co)homology over commutative DG-rings
Liran Shaul
Let be a commutative noetherian ring, let be an ideal, and let be an injective -module. A basic result in the structure theory of injective mod…
Completion and torsion over commutative DG rings
Liran Shaul
Let be the category whose objects are pairs , where is a commutative DG-algebra and $\bar{\mathfrak{a}}\subseteq \mathrm{H}^…
Adic reduction to the diagonal and a relation between cofiniteness and derived completion
Liran Shaul
We prove two results about the derived functor of -adic completion: (1) Let be a commutative noetherian ring, let be a flat noetherian -algebra which is -adically…
The twisted inverse image pseudofunctor over commutative DG rings and perfect base change
Liran Shaul
Let be a Gorenstein noetherian ring of finite Krull dimension, and consider the category of cohomologically noetherian commutative differential graded rings over , such…
Errata: On the Homology of Completion and Torsion
Marco Porta, Liran Shaul, Amnon Yekutieli
In this note we correct two errors in our paper "On the Homology of Completion and Torsion", arXiv:1010.4386, that appeared in Algebras and Representation Theory (2014).
Hochschild cohomology commutes with adic completion
Liran Shaul
For a flat commutative -algebra such that the enveloping algebra is noetherian, given a finitely generated bimodule , we show that the adic completion of t…
Tensor product of dualizing complexes over a field
Liran Shaul
Let be a field, and let be two locally noetherian -schemes (respectively -formal schemes) with dualizing complexes and respectively. We show that $R_X \…
Reduction of Hochschild cohomology over algebras finite over their center
Liran Shaul
We borrow ideas from Grothendieck duality theory to noncommutative algebra, and use them to prove a reduction result for Hochschild cohomology for noncommutative algebras which are…