Related papers: Derived categories of bifiltered complexes

Let $\mathcal C$ be closed symmetric monoidal Grothendieck category. We define the pure derived category with respect to the monoidal structure via a relative injective model category structure on the category $\mathbf{C}(\mathcal C)$ of…

We introduce a derived smooth duality functor on the unbounded derived category of smooth mod p representations of a p-adic Lie group. Using this functor we relate various subcategories of admissible complexes.

We offer streamlined proofs of fundamental theorems regarding the index theory for partial self-maps of an infinite set that are bijective between cofinite subsets.

A semiorthogonal decomposition for the bounded derived category (the category of perfect complexes in a non smooth case) of coherent sheaves on a Brauer Severi scheme is given. It relies on bounded derived categories (categories of perfect…

We prove that every filtered fiber functor on the category of dualizable representations of a smooth affine group scheme with enough dualizable representations comes from a graded fiber functor.

The theory of $N$-complexes is a generalization of both ordinary chain complexes and graded objects. Hence it yields deeper insight in the structure of these and offers a broader range of applications. This work generalizes the tensor…

In this paper we prove first a general theorem on semiorthogonal decompositions in derived categories of coherent sheaves for flat families over a smooth base. Based on the results of math.AG/0510670, we then show that the derived…

We prove two theorems on the derived categories of toric varieties, the existence of an exceptional collection consisting of sheaves for a divisorial extraction and the finiteness of Fourier-Mukai partners.

We investigate equivariant birational geometry of rational surfaces and threefolds from the perspective of derived categories.

In this article, we define the notion of a filtration and then give the basic theorems on initial and progressive enlargements of filtrations.

In this article, we study higher Nil $K$-groups via binary complexes. More particularly, we exhibit an explicit form of generators of higher Nil $K$-groups in terms of binary complexes.

In this paper, we study the structure of a generalized near-group fusion category and classified it when it is slightly degenerate.

This paper is a sequel to "t-structures and twisted complexes on derived injectives" by the same authors. We develop the foundations of the infinitesimal derived deformation theory of pretriangulated dg-categories endowed with t-structures.…

Our main theorem classifies the Auslander-Reiten triangles according to properties of the morphisms involved. As a consequence, we are able to compute the mapping cone of an irreducible morphism. We finish by showing a technique for…

We develop bicategory theory in univalent foundations. Guided by the notion of univalence for (1-)categories studied by Ahrens, Kapulkin, and Shulman, we define and study univalent bicategories. To construct examples of univalent…

A new class of 3-manifold invariants is constructed from representations of the category of framed tangles.

We show that the triangulated category of bounded constructible complexes on an algebraic variety X over an algebraically closed field is equivalent to the bounded derived category of the abelian category of constructible sheaves on X,…

Ultrafilters are useful mathematical objects having applications in nonstandard analysis, Ramsey theory, Boolean algebra, topology, and other areas of mathematics. In this note, we provide a categorical construction of ultrafilters in terms…

We develop the theory of cofinal types of ultrafilters over measurable cardinals and establish its connections to Galvin's property. We generalize fundamental results from the countable to the uncountable, but often in surprisingly…

We give a combinatorial model for the bounded derived category of graded modules over the dual numbers in terms of arcs on the integer line with a point at infinity. Using this model we describe the lattice of thick subcategories of the…