Related papers: Resolution of the Diagonal on the Root Stacks
We calculate a semi-orthogonal decomposition of the bounded derived category of coherent sheaves on P(1,1,1,3) using a tilting bundle.
We prove that the bounded derived category of coherent sheaves with proper support is equivalent to the category of locally-finite, cohomological functors on the perfect derived category of a quasi-projective scheme over a field. We…
We give a block decomposition of the dg category of character sheaves on a simple and simply-connected complex reductive group $G$, similar to the one in generalized Springer correspondence. As a corollary, we identify the category of…
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…
The central aim of this monograph is to provide decomposition results for quasi-coherent sheaves on the moduli stack of one-dimensional formal groups. These results will be based on the geometry of the stack itself, particularly the height…
We consider semi-orthogonal decompositions of derived categories for 3-dimensional projective varieties in the case when the varieties have ordinary double points.
Kuznetsov showed that for a flat quadric fibration $\mathcal{Q}$ over a smooth base $S$, $\mathrm{D}^b(\mathcal{Q})$ admits a semiorthogonal decomposition where one of the components is the derived category of the sheaf of even parts of a…
The purpose of this paper is to use conservative descent to study semi-orthogonal decompositions for some homogeneous varieties over general bases. We produce a semi-orthogonal decomposition for the bounded derived category of coherent…
This paper is devoted to constructing "new" admissible subcategories and semi-orthogonal decompositions of triangulated categories out of "old" ones. For two triangulated subcategories $T$ and $T'$ of a certain $D$ and a decomposition…
Consider an algebraic variety $X$ over a base scheme $S$ and a faithful base change $T \to S$. Given an admissible subcategory $\CA$ in the bounded derived category of coherent sheaves on $X$, we construct an admissible subcategory in the…
For an effective Cartier divisor D on a scheme X we may form an nth root stack. Its derived category is known to have a semiorthogonal decomposition with components given by D and X. We show that this decomposition is 2n-periodic. For n=2…
We assume given a smooth symplectic (in the algebraic sense) resolution $X$ of an affine algebraic variety $Y$, and we prove that, possibly after replacing $Y$ with an etale neighborhood of a point, the derived category of coherent sheaves…
We show the existence of semiorthogonal decompositions of Donaldson-Thomas categories for $(-1)$-shifted cotangent derived stacks associated with $\Theta$-stratifications on them. Our main result gives an analogue of window theorem for…
We show that the derived category of coherent sheaves on the quotient stack of the affine plane by a finite small subgroup of the general linear group is obtained from the derived category of coherent sheaves on the minimal resolution by…
We develop an approach that allows to construct semiorthogonal decompositions of derived categories of surfaces with cyclic quotient singularities whose components are equivalent to derived categories of local finite dimensional algebras.…
Using the description of the category of quasi-coherent sheaves on a root stack given in the paper of N. Borne and A. Vistoli, we study the G-theory of root stacks via localisation methods. We apply our results to the study of equivariant…
Let $\mathcal{X}$ be a smooth Deligne-Mumford stack which is generically a scheme and has quasi-projective coarse moduli. If $\mathcal{X}$ has elementary Abelian 2-group stabilizers and the coarse moduli of the inertia stack is smooth, we…
The aim of this note is to discuss resolution theorems that are useful in the study of semi log canonical varieties.
In this article, we investigate semi-orthogonal decompositions of the symmetric products of dg-enhanced triangulated categories. Given a semi-orthogonal decomposition $\mathcal{D}=\langle \mathcal{A}, \mathcal{B} \rangle$, we construct…
Motivated by the local flavor of several well-known semi-orthogonal decompositions in algebraic geometry, we introduce a technique called conservative descent, which shows that it is enough to establish these decompositions locally. The…