7 citations · 20 across the 18 of their papers we have counts for
21 papers
The embedded deformation problem for monomial ideals
Benjamin Briggs, Eloísa Grifo, Josh Pollitz
This article is concerned with homological properties of local or graded rings whose defining relations are monomials on some regular sequence. The main result of the article posit…
Classifying thick subcategories over a Koszul complex via the curved BGG correspondence
Jian Liu, Josh Pollitz
In this work we classify the thick subcategories of the bounded derived category of dg modules over a Koszul complex on any list of elements in a regular ring. This simultaneously…
Lower bounds on Loewy lengths of modules of finite projective dimension
Nawaj KC, Josh Pollitz
This article is concerned with nonzero modules of finite length and finite projective dimension over a local ring. We show the Loewy length of such a module is larger than the regu…
Relations between Poincaré series for quasi-complete intersection homomorphisms
Josh Pollitz, Liana M. Sega
In this article we study base change of Poincaré series along a quasi-complete intersection homomorphism , where is a local ring with maximal ideal $\mathfrak{…
Koszul homomorphisms and universal resolutions in local algebra
Benjamin Briggs, James C. Cameron, Janina C. Letz +1
We define a local homomorphism to be Koszul if its derived fiber is formal, and if is Koszul in the cla…
High Frobenius pushforwards generate the bounded derived category
Matthew R. Ballard, Srikanth B. Iyengar, Pat Lank +2
This work concerns generators for the bounded derived category of coherent sheaves over a noetherian scheme of prime characteristic. The main result is that when the Frobenius…
Bounds on cohomological support varieties
Benjamin Briggs, Eloísa Grifo, Josh Pollitz
Over a local ring , the theory of cohomological support varieties attaches to any bounded complex of finitely generated -modules an algebraic variety that encode…
Resolutions of differential operators of low order for an isolated hypersurface singularity
Rachel N. Diethorn, Jack Jeffries, Claudia Miller +4
In this paper we develop a new approach for studying differential operators of an isolated singularity graded hypersurface ring defining a surface in affine three-space over a…
Cohomological supports of tensor products of modules over commutative rings
Srikanth B. Iyengar, Josh Pollitz, William T. Sanders
This works concerns cohomological support varieties of modules over commutative local rings. The main result is that the support of a derived tensor product of a pair of differenti…
Cohomological jump loci and duality in local algebra
Benjamin Briggs, Daniel McCormick, Josh Pollitz
In this article a higher order support theory, called the cohomological jump loci, is introduced and studied for dg modules over a Koszul extension of a local dg algebra. The gener…
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 …
A comparison of dg algebra resolutions with prime residual characteristic
Michael DeBellevue, Josh Pollitz
In this article we fix a prime integer and compare certain dg algebra resolutions over a local ring whose residue field has characteristic . Namely, we show that given a clo…
Exceptional complete intersection maps of local rings
Srikanth B. Iyengar, Janina C. Letz, Jian Liu +1
This work concerns surjective maps of commutative noetherian local rings with kernel generated by a regular sequence that is part of a minimal generating set for t…
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…
A partial converse ghost lemma for the derived category of a commutative noetherian ring
Jian Liu, Josh Pollitz
In this article a condition is given to detect the containment among thick subcategories of the bounded derived category of a commutative noetherian ring. More precisely, for a com…
Constructing non-proxy small test modules for the complete intersection property
Benjamin Briggs, Eloísa Grifo, Josh Pollitz
A local ring is regular if and only if every finitely generated -module has finite projective dimension. Moreover, the residue field is a test module: is regular if…
Locally complete intersection maps and the proxy small property
Benjamin Briggs, Srikanth B. Iyengar, Janina C. Letz +1
It is proved that a map of commutative noetherian rings that is essentially of finite type and flat is locally complete intersection if and only is proxy small…
Duality and symmetry of complexity over complete intersections via exterior homology
Jian Liu, Josh Pollitz
We study homological properties of a locally complete intersection ring by importing facts from homological algebra over exterior algebras. One application is showing that the thic…
Cohomological supports over derived complete intersections and local rings
Josh Pollitz
A theory of cohomological support for pairs of DG modules over a Koszul complex is investigated. These specialize to the support varieties of Avramov and Buchweitz defined over a c…
Equivariant isomorphisms of Ext and Tor modules
Josh Pollitz
In this article we establish equivariant isomorphisms of Ext and Tor modules over different relative complete intersections. More precisely, for a commutative ring , this paper…
The derived category of a locally complete intersection ring
Josh Pollitz
In this paper, we answer a question of Dwyer, Greenlees, and Iyengar by proving a local ring is a complete intersection if and only if every complex of -modules with finitel…