Related papers: T-structures on the derived categories of D-module…

We construct an equivalence between the derived category of sheaves on an elliptic threefold without a section and a derived category of twisted sheaves (modules over an Azumaya algebra) on any small resolution of its relative Jacobian.

We propose a conjecture on the structure of the bounded derived category of coherent sheaves of the moduli space rank $2$ parabolic bundles on $\mathbb{P}^1$.

In this paper, we try to realize the unbounded derived category of an abelian category as the homotopy category of a Quillen model structure on the category of unbounded chain complexes. We construct such a model structure based on…

This paper is a contribution to the study of relative holonomic $\mathcal{D}$-modules. Contrary to the absolute case, the standard $t$-structure on holonomic $\mathcal{D}$-modules is not preserved by duality and hence the solution functor…

Based on the recent progress in the irregular Riemann-Hilbert correspondence for holonomic D-modules, we show that the characteristic cycles of some standard irregular holonomic D-modules can be expressed as in the classical theorem of…

We describe tilting modules of the deformed category O over a semisimple Lie algebra as certain sheaves on a moment graph associated to the corresponding block of category O. We prove that they map to Braden-MacPherson sheaves constructed…

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 describe the heart of the canonical $t$-structure on the perfect derived category of a strictly positive graded algebra as the module category over the quadratic dual. Applying this result we obtain examples showing new phenomena on…

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open…

Motivated by applications to the categorical and geometric local Langlands correspondences, we establish an equivalence between the category of filtered $\mathcal{D}$-modules on a smooth stack $X$ and the category of $S^1$-equivariant…

We explain the precise relationship between two module-theoretic descriptions of sheaves on an involutive quantale, namely the description via so-called Hilbert structures on modules and that via so-called principally generated modules. For…

Let $Z$ be a Fano variety satisfying the condition that the rank of the Grothendieck group of $Z$ is one more than the dimension of $Z$. Let $\omega_Z$ denote the total space of the canonical line bundle of $Z$, considered as a non-compact…

We study derived categories of coherent sheaves on abelian varieties. We give a criterion for the equivalence of the derived categories on two abelian varieties. We describe the autoequivalence group for the derived category of coherent…

We prove that the bounded derived category of coherent sheaves on a smooth projective complex variety reconstructs the isomorphism classes of fibrations onto smooth projective curves of genus $g\geq 2$. Moreover, in dimension at most four,…

Various topological properties of D-branes in the type--IIA theory are captured by the topologically twisted B-model, treating D-branes as objects in the bounded derived category of coherent sheaves on the compact part of the target space.…

Under a mild condition, the perfect derived category and the finite-dimensional derived category of a graded gentle one-cycle algebra are described as twisted root categories of certain infinite quivers of type $\mathbb{A}_\infty^\infty$.…

This note is mostly an exposition of an unpublished result of Deligne, which introduces an analogue of perverse $t$-structure on the derived category of coherent sheaves on a Noetherian scheme with a dualizing complex. Construction extends…

Starting point of the present work is a conjecture of F. Catanese which says that in the derived category of coherent sheaves on any rational homogeneous manifold G/P there should exist a complete strong exceptional poset and a bijection of…

For an embedding of sufficiently high degree of a smooth projective variety X into projective space, we use residues to define a filtered holonomic D-module (M, F) on the dual projective space. This gives a concrete description of the…

Let $d$ be a positive integer. In a previous article we established a bijective correspondence between the following classes of objects, considered up to the appropriate notion of equivalence: differential graded algebras with…