Related papers: Staggered t-structures on derived categories of eq…
We classify complactly generated t-structures on the derived category of modules over a commutative Noetherian ring R in terms of decreasing filtrations by supports on Spec(R). A decreasing filtration by supports \phi : Z -> Spec(R)…
The stable module category of a selfinjective algebra is triangulated, but need not have any nontrivial $t$-structures, and in particular, full abelian subcategories need not arise as hearts of a $t$-structure. The purpose of this paper is…
In this short paper we outline (mostly without proofs) our new approach to the derived category of sheaves of commutative DG rings. The proofs will appear in a subsequent paper. Among other things, we explain how to form the derived…
The aim of this paper is to present a recursive construction of simple t-designs for arbitrary t. The construction is of purely combinatorial nature and it requires finding solutions for the indices of the ingredient designs that satisfy a…
We prove that the categories of coherent sheaves over weighted projective lines of tubular type are explicitly related to each other via the equivariantization with respect to certain cyclic group actions.
The string group acts on the category of coherent sheaves over a weighted projective line by degree-shift actions. We study the equivariant equivalence relations induced by degree-shift actions between weighted projective lines. We prove…
We construct a weak representation of the category of framed affine tangles on a disjoint union of triangulated categories ${\mathcal D}_{2n}$. The categories we use are that of coherent sheaves on Springer fibers over a nilpotent element…
We define the derived category of quasi--coherent modules for certain Artin stacks as the homotopy category of two Quillen monoidal model structures on the corresponding category of unbounded complexes of quasi--coherent modules.
We construct derived fundamental group schemes for Tate motives over connected smooth schemes over fields. We show that there exists a pro affine derived group scheme over the rationals such that its category of perfect representations…
In the theory of triangulated categories, we propose to replace hearts of $t$-structures by proper abelian subcategories, which may be plentiful even when hearts are not. For instance, this happens in negative cluster categories. In support…
We define and study an exotic t-structure on the bounded derived category of equivariant coherent sheaves on partial resolutions of the nilpotent cone.
We investigate the bounded derived category of coherent sheaves on irreducible singular projective curves of arithmetic genus one. A description of the group of exact auto-equivalences and the set of all t-structures of this category is…
We consider deformations of G-structures via the right action on the frame bundle in a base-point-dependent manner. We investigate which of these deformations again lead to G-structures and in which cases the original and the deformed…
We introduce a notion of proxy smallness for $t$-structures on triangulated categories associated to a Noetherian scheme. Specifically, the theory is developed in the presence of tensor actions. Consequently, our results yield a new…
We show that perverse character varieties are (quasi-)affine. We do this in a purely stack-theoretic fashion, by exhibiting enough sections of the structure sheaf.
We propose to employ the hierarchical coarse-grained structure in the artificial neural networks explicitly to improve the interpretability without degrading performance. The idea has been applied in two situations. One is a neural network…
We discuss relations between the motives of two varieties with equivalent derived categories of coherent sheaves.
The present paper focuses on the study of t-stabilities on a triangulated category in the sense of Gorodentsev, Kuleshov and Rudakov. We give an equivalent description for the finest t-stability on a piecewise hereditary triangulated…
We study Gorenstein categories. We show that such a category has Tate cohomological functors and Avramov-Martsinkovsky exact sequences connecting the Gorenstein relative, the absolute and the Tate cohomological functors. We show that such a…
We study certain 'weights' for triangulated categories endowed with $t$-structures. Our results axiomatize and describe in detail the relations between the Chow weight structure (introduced in a preceding paper), the (conjectural) motivic…