Related papers: Local dualisable objects in local algebra

In this paper, we will consider derived equivalences for differential graded endomorphism algebras by Keller's approaches. First we construct derived equivalences of differential graded algebras which are endomorphism algebras of the…

We develop a correspondence between presentations of compactly generated triangulated categories as localizations of derived categories of ring spectra and proxy-small objects, and explore some consequences. In addition, we give a…

We describe (braided-)commutative algebras with non-degenerate multiplicative form in certain braided monoidal categories, corresponding to abelian metric Lie algebras (so-called Drinfeld categories). We also describe local modules over…

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 thick subcategories of the bounded derived category of a locally…

Let $\mathfrak{a}$ be an ideal of a local ring $(R, \mathfrak{m})$ with $c = \mathrm{cd}(\mathfrak{a},R)$ the cohomological dimension of $\mathfrak{a}$ in $R$. In the case that $c=\dim R$, we first give a bound for…

We consider the derived category of permutation modules for a finite group, in positive characteristic. We stratify this tensor triangulated category using Brauer quotients. We describe the spectrum of its compact objects, by reducing the…

Let $\mathscr{C}$ be a 2-Calabi-Yau triangulated category, and let $\mathscr{T}$ be a cluster tilting subcategory of $\mathscr{C}$. An important result from Dehy and Keller tells us that a rigid object $c \in \mathscr{C}$ is uniquely…

In this paper, we characterize several properties of commutative notherian local rings in terms of the left perpendicular category of the category of finitely generated modules of finite projective dimension. As an application we prove that…

Utilizing previously established results concerning costratification in relative tensor-triangular geometry, we classify the colocalizing subcategories of the singularity category of a locally hypersurface ring and then we generalize this…

This paper systematically develops a notion of regular sequences in the context of $R$-linear triangulated categories for a graded-commutative ring $R$. The notion has equivalent characterizations involving Koszul objects and local…

Matlis duals of local cohomology modules are investigated with respect to many different topics (see section 0 - Introduction). One of these topics are complete intersections - see Corollary 1.1.4.

We compute the local intersection cohomology of the irreducible components of varieties of complexes, by using Lusztig's geometric approach to quantum groups and explicit constructions of elements of Lusztig's canonical bases.

The paper is devoted to 2-local derivations on the algebra $LS(M)$ of all locally measurable operators affiliated with a type I$_\infty$ von Neumann algebra $M.$ We prove that every 2-local derivation on $LS(M)$ is a derivation.

Let $A$ be a noetherian ring, $\fa$ an ideal of $A$, and $M$ an $A$--module. Some uniform theorems on the artinianness of certain local cohomology modules are proven in a general situation. They generalize and imply previous results about…

In this paper, we are concerned with Gorenstein projective objects in homotopy categories. Specifically, we present a characterization on Gorenstein projective objects in the category of complexes. Using this result, it is proved that the…

We show that the following five categories are equivalent: (1) the opposite category of commutative von Neumann algebras; (2) compact strictly localizable enhanced measurable spaces; (3) measurable locales; (4) hyperstonean locales; (5)…

We give an elementary introduction to the theory of triangulated categories covering their axioms, homological algebra in triangulated categories, triangulated subcategories, and Verdier localization. We try to use a minimal set of axioms…

We give an account of model theory in the context of compactly generated triangulated and tensor-triangulated categories ${\cal T}$. We describe pp formulas, pp-types and free realisations in such categories and we prove elimination of…

In this paper we consider the classification of minimal cellular structures of spaces of topological complexity two under some hypotheses on there graded cohomological algebra. This continues the method used by M.Grant et al. in [1].

We give algorithms for the computation of the algebraic de Rham cohomology of open and closed algebraic sets inside projective space or other smooth complex toric varieties. The methods, which are based on Gr\"obner basis computations in…