Related papers: Cohen-Macaulay modules and the Bondal-Orlov conjec…

In this paper we completely classify all the special Cohen-Macaulay (=CM) modules corresponding to the exceptional curves in the dual graph of the minimal resolutions of all two dimensional quotient singularities. In every case we exhibit…

A causal manifold $(M,\gamma)$ is a manifold $M$ endowed with a closed proper cone $\gamma$ in the tangent bundle $TM$ such that the projection $TM\to M$ is surjective when restricted to the interior of $\gamma$. Let $\lambda$ be the…

For a locally presentable abelian category $\mathsf B$ with a projective generator, we construct the projective derived and contraderived model structures on the category of complexes, proving in particular the existence of enough homotopy…

An unrepresentable cohomological functor of finite type of the bounded derived category of coherent sheaves of a compact complex manifold of dimension greater than one with no proper closed subvariety is given explicitly in categorical…

We prove that moduli spaces of torsion-free sheaves on a projective smooth complex surface are irreducible, reduced and of the expected dimension, provided the expected dimension is large enough. Actually we prove more: given a line bundle…

We consider homological mirror symmetry in the context of hypertoric varieties, showing that appropriate categories of B-branes (that is, coherent sheaves) on an additive hypertoric variety match a category of A-branes on a Dolbeault…

In this short note, we classify linear categorified open topological field theories in dimension two by pivotal Grothendieck-Verdier categories, a type of monoidal category equipped with a weak, not necessarily rigid duality. In combination…

We classify all tilting and cotilting classes over commutative noetherian rings in terms of descending sequences of specialization closed subsets of the Zariski spectrum. Consequently, all resolving subcategories of finitely generated…

We show that various derived categories of torsion modules and contramodules over the adic completion of a commutative ring by a weakly proregular ideal are full subcategories of the related derived categories of modules. By the work of…

By results of Rognerud, a source algebra equivalence between two $p$-blocks of finite groups induces an equivalence between the categories of cohomological Mackey functors associated with these blocks, and a splendid derived equivalence…

In this article we study a relative monoidal version of the Bondal-Orlov reconstruction theorem. We establish an uniqueness result for tensor triangulated category structures $(\boxtimes,\mathbb{1})$ on the derived category $D^{b}(X)$ of a…

Let R be a non-negatively graded Cohen-Macaulay ring with R_0 a Cohen-Macaulay factor ring of a local Gorenstein ring. Let d be the dimension of R, m be the maximal homogeneous ideal of R, and M be a finitely generated graded R-module. It…

We prove that every simple flop of type $D_5$, i.e., resolved by blowups with exceptional divisor isomorphic to a generalized Grassmann bundle with fiber $OG(4, 10)$, induces a derived equivalence. This provides new evidence for the DK…

In this article we introduce a new class of non-commutative projective curves and show that in certain cases the derived category of coherent sheaves on them has a tilting complex. In particular, we prove that the right bounded derived…

Given a brane tiling, that is, a bipartite graph on a torus, we can associate with it a singular 3-Calabi-Yau variety. Using the brane tiling, we can also construct all crepant resolutions of the above variety. We give an explicit toric…

We consider closed manifolds that admit a metric locally isometric to a product of symmetric planes. For such manifolds, we prove that the Euler characteristic is an obstruction to the existence of flat structures, confirming an old…

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 consider a finite collection of line bundles $\Phi$ introduced by Bondal on a smooth, projective toric variety $X$. For any coherent sheaf $F$ on $X$, we construct minimal resolutions of $F$ by line bundles in $\Phi$, up to twist, with…

For a finite dimensional algebra $A$, we prove that the bounded homotopy category of projective $A$-modules and the bounded derived category of $A$-modules are dual to each other via certain categories of locally-finite cohomological…

Condensed mathematics as developed by Clausen and Scholze yields a version of derived functors over the category of continuous $G$-modules for a Hausdorff topological group $G$. We study the resulting notion of group cohomology and its…