Related papers: Recollements and homological dimensions
We determine the homological dimension of various isogeny categories of commutative algebraic groups over a field $k$, in terms of the cohomological dimension of $k$ at certain primes. This generalizes results of Serre, Oort and Milne, by…
Gorenstein homological dimensions are refinements of the classical homological dimensions, and finiteness singles out modules with amenable properties reflecting those of modules over Gorenstein rings. As opposed to their classical…
Let A be an algebra with a countable basis and let B be, say, a Frechet algebra that contains A as a dense subalgebra. This embedding induces a functor from the derived category of B-modules to the derived category of A-modules. In many…
The rigidity degree of a generator-cogenerator determines the dominant dimension of its endomorphism algebra, and is closely related to a recently introduced homological dimension -- rigidity dimension. In this paper, we give explicit…
In a general triangulated category, the finiteness of the finitistic dimension serves as a prerequisite for a categorical obstruction, via the singularity category, to the existence of bounded $t$-structures. In this paper, we investigate…
For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…
We propose a new method to investigate the dimension of the space of integrals on a Hopf algebra $H$ and other properties of $H$-comodules.
We use the machinery of relative homological algebra to study modules of finite Gorenstein flat dimension.
In Enochs' relative homological dimension theory occur the so called (co)resolvent and (co)proper dimensions which are defined using proper and coproper resolutions constructed by precovers and preenvelopes, respectively. Recently, some…
In the derived category of the category of modules over a commutative Noetherian ring $R$, we define, for an ideal $\fa$ of $R$, two different types of cohomological dimensions of a complex $X$ in a certain subcategory of the derived…
We aim at studying collections of algebraic structures defined over a commutative ring and investigating the complexity of significant constructions carried out on these objects. The assignment of measures of size, via a multiplicity…
In this paper we study derived equivalences between triangular matrix algebras using certain classical recollements. We show that special properties of these recollements actually characterize triangular matrix algebras, and describe…
In this paper, we first study the Gorenstein projective/flat dimension of complexes of modules. The relation between the Gorenstein projective/flat dimension for complexes and that for modules are investigated. Then we study Tate, stable…
We give a proof, based on the rigidity of tilting complexes, that the class of self-injective finite-dimensional algebras over an algebraically closed field is closed under derived equivalence.
We study endomorphism algebras of 2-term silting complexes in derived categories of hereditary finite dimensional algebras, or more generally of $\mathop{\rm Ext}\nolimits$-finite hereditary abelian categories. Module categories of such…
For an abelian category, a category equivalent to its derived category is constructed by means of specific projective (injective) multicomplexes, the so-called homological resolutions.
We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…
Recollements of abelian categories are used as a basis of a homological and recursive approach to quasi-hereditary algebras. This yields a homological proof of Dlab and Ringel's characterisation of idempotent ideals occuring in heredity…
We consider a class of extensions of associative algebras, which we refer to as ``strongly proj-bounded extensions''. We prove that the finiteness of the left global dimension and the support of the Hochschild homology is preserved by…
Let $R$ be a Noetherian ring and let $C$ be a semidualizing $R$-module. In this paper, by using the semidualizing modules, we define and study new classes of modules and homological dimensions and investigate the relations between them. In…