Related papers: Generators versus projective generators in abelian…

Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put…

For an exact category having enough projective objects, we establish a bijection between thick subcategories containing the projective objects and thick subcategories of the stable derived category. Using this bijection we classify thick…

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…

Let $A$ be a coherent algebra and $B$ be a finite-dimensional Gorenstein algebra over a field $k$. We describe finitely presented Gorenstein projective $A\otimes_k B$-modules in terms of their underlying onesided modules. Moreover, if the…

Given an abelian category A with enough projectives, we can form its stable category _A_ := A/Proj(A)$. The Heller operator Omega : _A_ -> _A_ is characterised on an object X by a choice of a short exact sequence Omega X -> P -> X in A with…

A finite tensor category is called pointed if all its simple objects are invertible. We find necessary and sufficient conditions for two pointed semisimple categories to be dual to each other with respect to a module category. Whenever the…

We determine Grothendieck groups of periodic derived categories. In particular, we prove that the Grothendieck group of the $m$-periodic derived category of finitely generated modules over an Artin algebra is a free $\mathbb{Z}$-module if…

We define the notion of an infinitely generated tilting object of infinite homological dimension in an abelian category. A one-to-one correspondence between $\infty$-tilting objects in complete, cocomplete abelian categories with an…

For a finite free and projective EI category, we prove that Gorenstein-projective modules over its category algebra are closed under the tensor product if and only if each morphism in the given category is a monomorphism.

We prove that any faithful Frobenius functor between abelian categories preserves the Gorenstein projective dimension of objects. Consequently, it preserves and reflects Gorenstein projective objects. We give conditions on when a Frobenius…

Similar to the idea of relative projectivity, we introduce the notion of relative subprojectivity, which is an alternative way to measure the projectivity of a module. Given modules $M$ and $N$, $M$ is said to be {\em $N$-subprojective} if…

For a non-Archimedean local field $F$ of residue cardinality $q=p^r$, we give an explicit classical generator $V$ for the bounded derived category $D_{fg}^b(\mathsf{H}_1(G))$ of finitely generated unipotent representations of…

We give an alternative proof to the fact that if the square of the infinite radical of the module category of an Artin algebra is equal to zero then the algebra is of finite type by making use of the theory of postprojective and…

We study the splitting-type of the bi-modules of principal parts (Grothendiecks analogue of jet-bundles in algebraic geometry) as left and right O-module on the projective line in positive characteristic, and obtain explicit examples where…

We study linear versions of Reedy categories in relation with finite dimensional algebras and abelian model structures. We prove that, for a linear Reedy category $\mathcal{C}$ over a field, the category of left $\mathcal{C}$--modules…

For an abelian category and a distinguished object with a graded endomorphism ring a necessary and sufficient criterion is given so that the category is equivalent to the abelian quotient of the category of finitely presented graded modules…

Suppose that $\mathcal{A}$ is an abelian category whose derived category $\mathcal{D}(\mathcal{A})$ has $Hom$ sets and arbitrary (small) coproducts, let $T$ be a (not necessarily classical) ($n$-)tilting object of $\mathcal{A}$ and let…

We study three related homological properties of modules in the BGG category O for basic classical Lie superalgebras, with specific focus on the general linear superalgebra. These are the projective dimension, associated variety and…

Modular functors are traditionally defined as systems of projective representations of mapping class groups of surfaces that are compatible with gluing. They can formally be described as modular algebras over central extensions of the…

For a rigid object $M$ in an algebraic triangulated category $\mathcal{T}$, a functor pr$(M)\to\mathcal{H}^{[-1,0]}({\rm proj}\, A)$ is constructed, which essentially takes an object to its `presentation', where pr$(M)$ is the full…