Related papers: $R$-linear triangulated categories and stability c…
We introduce the notion of relative stability conditions on triangulated categories with respect to left admissible subcategories, based on arXiv:math/0212237, and demonstrate the deformation of relative stability conditions via the…
We study some examples of Bridgeland-Douglas stability conditions on triangulated categories. From one side we give a complete description of the stability manifolds for smooth projective curves of positive genus. From the other side we…
The space of Bridgeland stability conditions is a complex manifold that can be attached to a triangulated category, of which it encodes some homological properties. These notes are an introduction to this topic, with a focus on examples…
We propose the notion of stability on a triangulated category that is a generalization of the T.Bridgeland's stability data. We establish connections between stabilities and t-structures on a category and as application we get the…
Stability conditions on triangulated categories were introduced by Bridgeland as a 'continuous' generalisation of t-structures. The set of locally-finite stability conditions on a triangulated category is a manifold which has been studied…
This paper introduces the notion of a stability condition on a triangulated category. The motivation comes from the study of Dirichlet branes in string theory, and especially from M.R. Douglas's notion of $\Pi$-stability. From a…
We introduce two extensions of the space of Bridgeland stability conditions of a triangulated category. First we consider lax stability conditions where semistable objects are allowed to have mass zero but still have a phase. The…
We define and study a gluing procedure for Bridgeland stability conditions in the situation when a triangulated category has a semiorthogonal decomposition. As an application we construct stability conditions on the derived categories of…
A triangulated category $\mathcal{C}$ with a canonical Bott's isomorphism $[2]\xrightarrow{\sim}id$ is called a cyclic category in this paper. We give a new notion of stability conditions on a $k$-linear Krull-Schmidt cyclic category. Given…
We exhibit examples of triangulated categories which are neither the stable category of a Frobenius category nor a full triangulated subcategory of the homotopy category of a stable model category. Even more drastically, our examples do not…
In this note, I define a notion of a compactly supported object in a triangulated category. I prove a number of propositions relating this to traditional notions of support and give an application to the theory of derived Morita…
We provide an axiomatic approach for studying support varieties of objects in a triangulated category via the action of a tensor triangulated category, where the tensor product is not necessarily symmetric. This is illustrated by examples,…
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…
In this paper, we give a definition of weak stability condition on a triangulated category. The difference between our definition and existing definitions is that we allow objects in the kernel to have non-maximal phases. We then construct…
These are notes of a course given at the 'school on moduli spaces' at the Newton Institute in January 2011. The abstract theory of stability conditions (due to Bridgeland and Douglas) on abelian and triangulated categories is developed via…
In this article, we treat stability conditions in the sense of King, Bridgeland and Bayer in a single framework. Following King, we begin with weight functions on a triangulated category, and consider increasingly specialised configurations…
We describe spaces of Bridgeland stability conditions on certain triangulated categories associated to Coxeter systems. These categories are defined algebraically using the category of modules for zigzag algebras associated to Coxeter…
Let $R$ be a commutative ring If $\mathcal{C}_1$ and $\mathcal{C}_2$ are $R$-linear triangulated categories then we can give an obvious triangulated structure on $\mathcal{C} = \mathcal{C}_1 \oplus \mathcal{C}_2$ where $Hom_\mathcal{C}(U,…
We revisit a result of Gratz and Stevenson on the universal space that carries supports for objects of a triangulated category, in the absence of a tensor product.
In this paper, as an analogue of the spectrum of a tensor triangulated category introduced by Balmer, we define a spectrum of a triangulated category which does not necessarily admit a tensor structure. We apply it for some triangulated…