Related papers: Twisted derived categories and Rouquier functors
We give the description of the t-structure on the derived category of regular holonomic D-modules corresponding to the trivial t-structure on the derived category of constructible sheaves via Riemann-Hilbert correspondence. We give also the…
We generalize a classical result about the genus of curves in projective space by Gruson and Peskine to principally polarized abelian threefolds of Picard rank one. The proof is based on wall-crossing techniques for ideal sheaves of curves…
Using a quiver algebra of a cyclic quiver, we construct a faithful categorical action of the extended braid group of affine type A on its bounded homotopy category of finitely generated projective modules. The algebra is trigraded and we…
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,…
We prove that the neutral component of the group of derived autoequivalences of a smooth projective variety is the semi-direct product of the neutral component of its Picard group and its group of automorphisms. We use this result to prove…
In this article we construct a categorical resolution of singularities of an excellent reduced curve $X$, introducing a certain sheaf of orders on $X$. This categorical resolution is shown to be a recollement of the derived category of…
B-fields over a groupoid with involution are defined as Real graded Dixmier-Douady bundles. We use these to introduce the Real graded Brauer group which constitutes the set of twistings for Atiyah's KR-functor in the category of locally…
In this thesis we study two main topics which culminate in a proof that four distinct definitions of the equivariant derived category of a smooth algebraic group $G$ acting on a variety $X$ are in fact equivalent. In the first part of this…
This paper classifies a class of holomorphic D-branes, closely related to framed torsion-free sheaves, on threefolds fibered in resolved ADE surfaces over a general curve C, in terms of representations with relations of a twisted…
We study triangulated categories which can be modeled by an oriented marked surface $\mathcal{S}$ and a line field $\eta$ on $\mathcal{S}$. This includes bounded derived categories of gentle algebras and -- conjecturally -- all partially…
Given a rigidly-compactly generated tensor-triangulated category whose Balmer spectrum is finite dimensional and Noetherian, we construct a torsion model for it, which is equivalent to the original tensor-triangulated category. The torsion…
We continue the study of twisted automorphisms of Hopf algebras started in "Twisted automorphisms of Hopf algebras". In this paper we concentrate on the group algebra case. We describe the group of twisted automorphisms of the group algebra…
In this paper we describe how Grothendieck groups of coherent sheaves and locally free sheaves can be used to describe type II D-branes, in the case that all D-branes are wrapped on complex varieties and all connections are holomorphic. Our…
Twisted diagrams are "diagrams" with components in different categories. Structure maps are defined using auxiliary data which consists of functors relating the various categories to each other. Prime examples of the construction are…
We develop sheaf theory in the context of difference algebraic geometry. We introduce categories of difference sheaves and develop the appropriate cohomology theories. As specializations, we get difference Galois cohomology, difference…
Studying crepant blow-ups of (compound) du Val singularities, we classify complexes of coherent sheaves which admit no negative self-extensions -- such a complex, up to flops and mutation equivalences, must either be (1) a module over a…
In this work more questions arise than answers given, for which of course we do not apologize. The core of this paper is concerned with the construction of a ``constant'' t-structure on the bounded derived category of coherent sheaves…
This work demonstrates classical generation is preserved by the derived pushforward along the structure morphism of a noncommutative coherent algebra to its underlying scheme. Additionally, we establish that the Krull dimension of a variety…
We prove that the Kuznetsov component of a flat family of even-dimensional quadrics of corank at most 2 is equivalent to the twisted derived category of an algebraic space whenever: (i) the open subset of the base over which the quadrics…
This paper surveys the recent advances concerning the relations between triangulated (or derived) categories and their dg enhancements. We explain when some interesting triangulated categories arising in algebraic geometry have a unique dg…