Related papers: Localization functors and cosupport in derived cat…

We classify certain resolving subcategories of finitely generated modules over a commutative noetherian ring R by using integer-valued functions on Spec R. As an application we give a complete classification of resolving subcategories when…

A notion of stratification is introduced for any compactly generated triangulated category T endowed with an action of a graded commutative noetherian ring R. The utility of this notion is demonstrated by establishing diverse consequences…

This is the second paper in a series to study regular representations for vertex operator algebras. In this paper, given a module $W$ for a vertex operator algebra $V$, we construct, out of the dual space $W^{*}$, a family of canonical…

This paper establishes a second vanishing theorem for formal local cohomology modules over Noetherian local rings. We introduce the \textit{formal dimension} invariant and characterize the vanishing of higher formal local cohomology in…

Let $R$ be a commutative Noetherian ring and $M$ a finitely generated $R$-module. We show in this paper that, for an integer $t$, if the local cohomology module $H^{i}_\mathfrak{a}(M)$ with respect to an ideal $\frak a$ is finitely…

We extend the support theory of Benson--Iyengar--Krause to the non-Noetherian setting by introducing a new notion of small support for modules. This enables us to prove that the stable module category of a finite group is canonically…

Let A be a commutative noetherian ring. In this paper, we interpret localizing subcategories of the derived category of A by using subsets of Spec A and subcategories of the category of A-modules. We unify theorems of Gabriel, Neeman and…

We construct a canonical pseudofunctor ^# on the category of finite-type maps of (say) connected noetherian universally catenary finite-dimensional separated schemes, taking values in the category of Cousin complexes. This pseudofunctor is…

Let $(R,\fr m)$ be a Noetherian local ring, $I$ an ideal of $R$ and $M, N$ two finitely generated $R$-modules. The first result of this paper is to prove a vanishing theorem for generalized local cohomology modules which says that…

Given a bounded complex of finitely generated modules $M$ over a commutative noetherian local ring $R$, one assigns to it a variety, $\mathcal V_R(M)$, called the cohomological support variety of $M$ over $R$. The variety $\mathcal V_R(M)$…

Let $k$ be a commutative $\mathbb{Q}$-algebra. We study families of functors between categories of finitely generated $R$-modules which are defined for all commutative $k$-algebras $R$ simultaneously and are compatible with base changes.…

Let R be a commutative Noetherian local ring. We show that R is Gorenstein if and only if every finitely generated R-module can be embedded in a finitely generated R-module of finite projective dimension. This extends a result of Auslander…

For a noetherian ring $\Lambda$, the stabilization functor in the sense of Krause yields an embedding of the singularity category of $\Lambda$ into the homotopy category of acyclic complexes of injective $\Lambda$-modules. When $\Lambda$…

Let A be the local ring at a point of a normal complex variety with completion R. Srinivas has asked about the possible images of the induced map from Cl A to Cl R over all geometric normal domains A with fixed completion R. We use…

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 Derived Depth Formula, itself an extension of Auslander famous…

Let $(R,\mathfrak{m})$ be a Noetherian local ring and $I$ an ideal of $R$. We study how local cohomology modules with support in $\mathfrak{m}$ change for small perturbations $J$ of $I$, that is, for ideals $J$ such that $I\equiv J\bmod…

For any dg algebra $A$, not necessarily commutative, and a subset $S$ in $H(A)$, the homology of $A$, we construct its derived localisation $L_S(A)$ together with a map $A\to L_S(A)$, well-defined in the homotopy category of dg algebras,…

Let $W$ be a complex reflection group of the form $G(l,1,n)$. Following [BK12, BPW12, Gor06, GS05, GS06, KR08, MN11], the theory of deform quantising conical symplectic resolutions allows one to study the category of modules for the…

Let $R$ be a ring and denote by $\mathcal{FM}$ the class of all flat and Mittag-Leffler left $R$-modules. In \cite{BazzoniStovicek2} it is proved that, if $R$ is countable, the orthogonal class of $\mathcal{FM}$ consists of all cotorsion…

Slicing a module into semisimple ones is useful to study modules. Loewy structures provide a means of doing so. To establish the Loewy structures of projective modules over a finite dimensional symmetric algebra over a field $F$, the…