Related papers: Remarks on generators and dimensions of triangulat…
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 prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…
Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived…
Building on Olander's work on algebraic spaces, we prove Orlov's representability theorem relating fully faithful functors and Fourier--Mukai transforms between the bounded derived category of coherent sheaves to the case of smooth, proper,…
Using derived categories of equivariant coherent sheaves, we construct a categorification of the tangle calculus associated to sl(2) and its standard representation. Our construction is related to that of Seidel-Smith by homological mirror…
We introduce the notion of a quasicoherent sheaf on a complex noncommutative two-torus $T$ as an ind-object in the category of holomorphic vector bundles on $T$. Extending the results of math.QA/0211262 and math.QA/0308136 we prove that the…
In this paper, using the quantum McKay correspondence, we construct the "derived category" of G-equivariant sheaves on the quantum projective line at a root of unity. More precisely, we use the representation theory of U_{q}sl(2) at root of…
Let $A$ be a graded algebra. It is shown that the derived category of dg modules over $A$ (viewed as a dg algebra with trivial differential) is a triangulated hull of a certain orbit category of the derived category of graded $A$-modules.…
We introduce new enhancements for the bounded derived category $D^b(Coh(X))$ of coherent sheaves on a suitable scheme $X$ and for its subcategory $Perf(X)$ of perfect complexes. They are used for translating Fourier-Mukai functors to…
In this paper, we consider how the approach of Bezrukavnikov and Kaledin to understanding the categories of coherent sheaves on symplectic resolutions can be applied to the Coulomb branches introduced by Braverman, Finkelberg and Nakajima.…
We construct a twist-closed enhancement of the category ${\mathcal D}^b_{\rm coh}(X)$, the bounded derived category of complexes of ${\mathcal O}_X$-modules with coherent cohomology, by means of the DG-category of…
In this paper, we classify several subcategories of the category of coherent sheaves on a noetherian divisorial scheme (e.g. a quasi-projective scheme over a commutative noetherian ring). More precisely, we classify the torsionfree (resp.…
We establish an equivalence between the stable category of coherent sheaves (satisfying a mild restriction) on a projective space and the homotopy category of a certain class of minimal complexes of free modules over the exterior algebra…
It is an open conjecture of Orlov that the bounded derived category of coherent sheaves of a smooth projective variety determines its Chow motive with rational coefficients. In this master's thesis we introduce a category of \emph{perfect…
This paper contains a description of one connected component of the space of stability conditions on the bounded derived category of coherent sheaves on a complex algebraic K3 surface.
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…
A new section on projections of coherent sheaves from a projective space to a lower-dimensional projective space has been added. Also some of the notation has been altered to bring it into line with the joint paper with Eisenbud and…
We give a simple proof for the rigidity of a complex in the bounded derived category of sheaves with constructible cohomology on an abelian variety.
Recollements of triangulated categories may be seen as exact sequences of such categories. Iterated recollements of triangulated categories are analogues of geometric or topological stratifications and of composition series of algebraic…
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…