Related papers: Killing weights from the perspective of t-structur…

We ask whether a morphism $g$ in a triangulated category $C$ endowed with a weight structure "kills weights" (between an integer $m$ and some $n\ge m$). If $g=id_M$ (where $M\in Obj C$) and $C$ is Karoubian, then $g$ kills weights…

We study "canonical weight decompositions" slightly generalizing that defined by J. Wildeshaus. For an triangulated category $C$, any integer $n$, and a weight structure $w$ on $C$ a triangle $LM\to M\to RM\to LM[1]$, where $LM$ is of…

This paper is dedicated to the study of weight complexes (defined on triangulated categories endowed with weight structures) and their applications. We introduce pure (co)homological functors that "ignore all non-zero weights"; these have a…

This paper is dedicated to new methods of constructing weight structures and weight-exact localizations; our arguments generalize their bounded versions considered in previous papers of the authors. We start from a class of objects $P$ of…

This paper is dedicated to triangulated categories endowed with weight structures (a new notion; D. Pauksztello has independently introduced them as co-t-structures). This axiomatizes the properties of stupid truncations of complexes in…

This article provides some basic results on weight structures, weight complex functors and homotopy categories. We prove that the full subcategories K(A)^{w < n}, K(A)^{w > n}, K(A)^- and K(A)^+ (of objects isomorphic to suitably bounded…

This is a survey of author's results on weight structures and Voevodsky's motives. Weight structures are natural counterparts of t-structures (for triangulated categories) introduced by the author. They allow to construct weight complexes,…

In this paper the complete geometrical setting of (lowest order) abelian T-duality is explored with the help of some new geometrical tools (the reduced formalism). In particular, all invariant polynomials (the integrands of the…

This paper classifies spherical objects in various geometric settings in dimensions two and three, including both minimal and partial crepant resolutions of Kleinian singularities, as well as arbitrary flopping 3-fold contractions with only…

In this paper certain Chow weight structures on the "big" triangulated motivic categories $DM_R^{eff}\subset DM_R$ are defined in terms of motives of all smooth varieties over the base field. This definition allows studying basic properties…

We develop the technique of weight truncation in the context of wall-crossings in birational cobordisms, parallel to that in [HL15, BFK19]. More precisely, for each such wall-crossing, we embed the bounded above derived category of coherent…

We define exact weights on a triangulated category to be nonnegative functions on objects satisfying a subadditivity condition with respect to exact triangles. Such weights induce a metric on objects in the triangulated category, which we…

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 develop a theory of completeness for weight structures on stable categories, dual to the theory of complete t-structures. As in the bounded case, we show that complete weight structures are determined by their weight heart, giving rise…

We consider all Bott-Samelson varieties ${\rm BS}(s)$ for a fixed connected semisimple complex algebraic group with maximal torus $T$ as the class of objects of some category. The class of morphisms of this category is an extension of the…

We study $t$-structures (on triangulated categories) that are closely related to weight structures. A $t$-structure couple $t=(C_{t\le 0},C_{t\ge 0})$ is said to be adjacent to a weight structure $w=(C_{w\le 0}, C_{w\ge 0})$ if $C_{t\ge…

We study t-structures generated by sets of objects which satisfy a condition weaker than the compactness. We also study weight structures cogenerated by sets of objects satisfying the dual condition. Under some appropriate hypothesis, it…

As we proved earlier, for a triangulated category $\underline{C}$ endowed with a weight structure $w$ and a triangulated subcategory $\underline{D}$ of $\underline{C}$ (strongly) generated by cones of a set of morphisms $S$ in the heart…

Let k be a finite field of characteristic p>0. We construct a theory of weights for overholonomic complexes of arithmetic D-modules with Frobenius structure on varieties over k. The notion of weight behave like Deligne's one in the l-adic…

In this paper we consider the structure of general quantum W-algebras. We introduce the notions of deformability, positive-definiteness, and reductivity of a W-algebra. We show that one can associate a reductive finite Lie algebra to each…