Related papers: On the derived category of a regular toric scheme

Let (X, O_X) be a noetherian formal scheme and consider D_qct(X) its derived category of sheaves with quasi-coherent torsion homology. We show that there is a bijection between the set of rigid (i.e. \tensor-ideals) localizing subcategories…

We present a homotopy theory for a weak version of modular operads whose compositions and contractions are only defined up to homotopy. This homotopy theory takes the form of a Quillen model structure on the collection of simplicial…

Exact categories are a natural generalisation of abelian categories and provide a fertile ground to develop relative homological algebra. In this paper, starting from a class of relative Gorenstein projective objects in an exact category…

We prove generating series formulae for suitable twisted characteristic classes of symmetric products of a singular complex quasi-projective variety. More concretely, we study homology Hirzebruch classes for motivic coefficients, as well as…

For a weighted projective line X, a wide subcategory of the category coh-X of coherent sheaves over X is called c-invariant if it is closed under the grading shift of the canonical element c. We proved that a c-invariant wide subcategory of…

In this paper, we study the category of twisted sheaves over a scheme $X$. Let $\mathcal{M}$ be a quasi-coherent sheaf on $X$, and $\alpha$ in $\operatorname{Br}(X)$. We show that the functor $ - \otimes_{\mathcal{O}_X} \mathcal{M} :…

We introduce the notion of a higher covering diagram in a base $\infty$-category $\mathcal{C}$. The theory of higher covering diagrams in $\mathcal{C}$ will be shown to recover various descent conditions known from the $\infty$-categorical…

We construct a cofibrantly generated model structure on the category of differential non-negatively graded quasi-coherent commutative $D_X$-algebras, where $D_X$ is the sheaf of differential operators of a smooth afine algebraic variety X.…

An important step towards the classification of finite-dimensional pointed Hopf algebras is the classification of finite-dimensional Nichols algebras arising from braided vector spaces of group type. This question is fundamentally linked…

We study moduli spaces of twisted quasimaps to a hypertoric variety $X$, arising as the Higgs branch of an abelian supersymmetric gauge theory in three dimensions. These parametrise general quiver representations whose building blocks are…

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…

Let G be a simple simply-connected group over an algebraically closed field k, X be a smooth connected projective curve over k. In this paper we develop the theory of geometric Eisenstein series on the moduli stack Bun_G of G-torsors on X…

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…

The first goal of this paper is to provide an abstract framework in which to formulate and study local duality in various algebraic and topological contexts. For any stable $\infty$-category $\mathcal{C}$ together with a collection of…

We investigate Hochschild cohomology and homology of admissible subcategories of derived categories of coherent sheaves on smooth projective varieties. We show that the Hochschild cohomology of an admissible subcategory is isomorphic to the…

The main aim of this paper is to study chains of model structures arising from cotorsion pairs in extriangulated categories. Starting with a hereditary Hovey triple, we construct further hereditary Hovey triples whose homotopy categories…

Let $R$ be any ring with identity. We show that the homotopy category of all acyclic chain complexes of pure-projective $R$-modules is a compactly generated triangulated category. We do this by constructing abelian model structures that put…

To any affine scheme with a $\mathbb{G}_m$-action, we provide a Bousfield colocalization on the equivariant derived category of modules by constructing, via homotopical methods, an idempotent integral kernel. This endows the equivariant…

We establish a unified group-theoretic framework bridging the arithmetic homotopy exact sequence of a variety and the Birman exact sequence of a surface. Within this framework, we reinterpret classical arithmetic notions - such as the…

We present a functorial computation of the equivariant intersection cohomology of a hypertoric variety, and endow it with a natural ring structure. When the hyperplane arrangement associated with the hypertoric variety is unimodular, we…