Related papers: A Note on Support in Triangulated Categories
We define and characterise small support for complexes over non-Noetherian rings and in this context prove a vanishing theorem for modules. Our definition of support makes sense for any rigidly compactly generated tensor triangulated…
We prove two results from Morita theory of stable model categories. Both can be regarded as topological versions of recent algebraic theorems. One is on recollements of triangulated categories, which have been studied in the algebraic case…
The concept of a morphism determined by an object provides a method to construct or classify morphisms in a fixed category. We show that this works particularly well for triangulated categories having Serre duality. Another application of…
We introduce and study several homological notions which generalise the discrete derived categories of D. Vossieck. As an application, we show that Vossieck discrete algebras have this property with respect to all bounded t-structures. We…
In spite of physics terms in the title, this paper is purely mathematical. Its purpose is to introduce triangulated categories related to singularities of algebraic varieties and establish a connection of these categories with D-branes in…
On objects of a triangulated category with a stability condition, we construct a topology.
We compare the homological support and tensor triangular support for `big' objects in a rigidly-compactly generated tensor triangulated category. We prove that the comparison map from the homological spectrum to the tensor triangular…
This paper develops a theory of pretriangulated 2-representations of dg 2-categories. We characterize cyclic pretriangulated 2-representations, under certain compactness assumptions, in terms of dg modules over dg algebra 1-morphisms…
We give an overview of recent developments in silting theory. After an introduction on torsion pairs in triangulated categories, we discuss and compare different notions of silting and explain the interplay with t-structures and…
We develop Tannaka duality theory for dg categories. To any dg functor from a dg category $\mathcal{A}$ to finite-dimensional complexes, we associate a dg coalgebra $C$ via a Hochschild homology construction. When the dg functor is…
In the work of Hoshino, Kato and Miyachi, the authors look at t-structures induced by a compact object, C, of a triangulated category, T, which is rigid in the sense of Iyama and Yoshino. Hoshino, Kato and Miyachi show that such an object…
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…
In this article, we introduce the notion of {\it concentric twin cotorsion pair} on a triangulated category. This notion contains the notions of $t$-structure, cluster tilting subcategory, co-$t$-structure and functorally finite rigid…
We give a general parametrization of all the recollement data for a triangulated category with a set of generators. From this we deduce a characterization of when a perfectly generated (or aisled) triangulated category is a recollement of…
In this work we consider the question of realizing triangulated dg-categories by derived categories of algebraic varieties. For this, we introduce the notion of "system of points" in saturated dg-categories. We show that given such a system…
We introduce the notion of categorical absorption of singularities: an operation that removes from the derived category of a singular variety a small admissible subcategory responsible for singularity and leaves a smooth and proper…
In this survey we present the relatively new concept of \emph{approximable triangulated categories.} We will show that the definition is natural, that it leads to powerful new results, and that it throws new light on old, familiar objects.…
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 establish a dual framework for Neeman's results concerning triangulated categories with compact silting objects by employing Brown--Comenetz duality. This framework introduces an intrinsic non-compact subcategory, provides…
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…