相关论文: A reduction approach to silting objects for derive…

In this work, we provide a simple way to construct $d$-abelian categories via bounded derived categories for certain values of $d$. Namely, let ${\mathcal C}$ be an abelian category, and let ${\mathcal C}[0,m]$ denote the full subcategory…

For a finite dimensional hereditary algebra, we consider: exceptional sequences in the category of finite dimensional modules, silting objects in the bounded derived category, and m-cluster tilting objects in the m-cluster category. There…

Let $A$ be a finite dimensional algebra over a field $k$ and $\textbf{P}$ be a 2-term silting complex in $K^{b}(\text{proj}A)$. In this paper, we investigate the representation dimension of $\text{End}_{D^{b}(A)} (\textbf{P})$ by using the…

We show that the category of orbits of the bounded derived category of a hereditary category under a well-behaved autoequivalence is canonically triangulated. This answers a question by A. Buan, R. Marsh and I. Reiten which appeared in…

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also the universal localisations of a hereditary ring, or…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

A general method for lifting weak factorization systems in a category S to model category structures on simplicial objects in S is described, analogously to the lifting of cotorsion pairs in Abelian categories to model category structures…

An abelian category with arbitrary coproducts and a small projective generator is equivalent to a module category \cite{Mit}. A tilting object in a abelian category is a natural generalization of a small projective generator. Moreover, any…

We use recollement and HRS-tilt to describe bounded t-structures on the bounded derived category $\mathcal{D}^b(\mathbb{X})$ of coherent sheaves over a weighted projective line $\mathbb{X}$ of virtual genus $\leq 1$. We will see from our…

We give a short proof to the following tilting theorem by Happel, Reiten and Smal{\o} via an explicit construction: given two abelian categories $\mathcal{A}$ and $\mathcal{B}$ such that $\mathcal{B}$ is tilted from $\mathcal{A}$, then…

Bijective correspondences are established between (1) silting objects, (2) simple-minded collections, (3) bounded $t$-structures with length heart and (4) bounded co-$t$-structures. These correspondences are shown to commute with mutations.…

Let k be an algebraically closed subfield of the complex numbers, and X a variety defined over k. One version of the Beilinson-Hodge conjecture that seems to survive scrutiny is the statement that the Betti cycle class map cl_{r,m} :…

We propose a geometric and categorical approach to the Hodge Conjecture for all smooth projective complex varieties. By embedding any such variety into a flat family with general fibers smooth complete intersections, we prove the conjecture…

A triangulated category $\mathcal{T}$ whose suspension functor $\Sigma$ satisfies $\Sigma^m \simeq \mathrm{Id}_{\mathcal{T}}$ as additive functors is called an $m$-periodic triangulated category. Such a category does not have a tilting…

Let $\mathcal{H}$ be a connected hereditary abelian category with tilting objects. It is proved that the cluster-tilting graph associated with $\mathcal{H}$ is always connected. As a consequence, we establish the connectedness of the…

A gentle algebra gives rise to a dissection of an oriented marked surface with boundary into polygons and the bounded derived category of the gentle algebra has a geometric interpretation in terms of this surface. In this paper we study…

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.

By a result of Orlov there always exists an embedding of the derived category of a finite-dimensional algebra of finite global dimension into the derived category of a high-dimensional smooth projective variety. In this article we give some…

Let $A$ be a hereditary algebra over an algebraically closed field $k$ and $A^{(m)}$ be the $m$-replicated algebra of $A$. Given an $A^{(m)}$-module $T$, we denote by $\delta (T)$ the number of non isomorphic indecomposable summands of $T$.…

Inspired by recent work of Bridgeland, from the category C^b(E) of bounded complexes over an exact category E satisfying certain finiteness conditions, we construct an associative unital "semi-derived Hall algebra" SDH(E). This algebra is…