Related papers: On flat generators and Matlis duality for quasicoh…

We develop techniques for constructing model structures on chain complexes valued in accessible exact categories, and apply this to show that for a closed symmetric monoidal, locally presentable exact category $\mathpzc{E}$ with exact…

We show that for every quasivariety K of structures (where both functions and relations are allowed) there is a semilattice S with operators such that the lattice of quasi-equational theories of K (the dual of the lattice of…

In this paper we prove that the dimension of the bounded derived category of coherent sheaves on a smooth quasi-projective curve is equal to one. We also discuss dimension spectrums of these categories.

In this note we extend the main results of [E. Enochs and S. Estrada, Relative homological algebra in the category of quasi-coherent sheaves. Adv. in Math. 194(2005), 284-295] to the category of cartesian modules over a flat presheaf of…

For any abelian category \calC satsifying (AB5) over a separated, quasi-compact scheme S, we construct a stack of 2-groups \GL(\calC) over the flat site of S. We will give a concrete description of \GL(\calC) when \calC is the category of…

Let $R$ be a ring and Ch($R$) the category of chain complexes of $R$-modules. We put an abelian model structure on Ch($R$) whose homotopy category is equivalent to $K(Proj)$, the homotopy category of all complexes of projectives. However,…

Realizing a part of the Derived Deformation Theory program, we construct a "derived" analog of the Grothendieck's Quot scheme parametrizing subsheaves in a given coherent sheaf F on a smooth projective variety X. This analog is a…

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…

If $X$ is the attractor set of a conformal IFS in dimension two or three, we prove that there exists a quasiregular semigroup $G$ with Julia set equal to $X$. We also show that in dimension two, with a further assumption similar to the open…

We prove a sheaf-theoretic derived-category generalization of Greenlees-May duality (a far-reaching generalization of Grothendieck's local duality theorem): for a quasi-compact separated scheme X and a "proregular" subscheme Z---for…

The purpose of this short note is to study Serre functors of categories of quasicoherent sheaves on stacks of the form $\mathcal{Y} = \mathrm{Spec} A/G$ where $G$ is a reductive group acting on $\mathrm{Spec} A$ with a unique closed orbit.…

We observe that for a quasi-compact and quasi-separated scheme the structure sheaf generates the perfect complexes if and only if the lattice of thick subcategories is distributive if and only if the affinization map is 0-affine. Examples…

This thesis deals with the algorithmic representation of constructible sheaves of abelian groups on the \'etale site of a variety over an algebraically closed field, as well as the explicit computation of their cohomology. We describe three…

The category of coherent sheaves over a noetherian scheme is very important for studying the properties of a given scheme. For noetherian schemes it is a well-known fact that the topology can be fully recovered from the corresponding…

Consider a complete abelian category which has an injective cogenerator. If its derived category is left--complete we show that the dual of this derived category satisfies Brown representability. In particular this is true for the derived…

Given a quasiprojective algebraic variety with a reductive group action, we describe a relationship between its equivariant derived category and the derived category of its geometric invariant theory quotient. This generalizes classical…

For a noetherian scheme that has an ample family of invertible sheaves, we prove that direct products in the category of quasi-coherent sheaves are not exact unless the scheme is affine. This result can especially be applied to all…

Part I proved that for every quasivariety K of structures (which may have both operations and relations) there is a semilattice S with operators such that he lattice of quasi-equational theories of K (the dual of the lattice of…

Contraherent cosheaves are globalizations of contraadjusted or cotorsion modules over commutative rings obtained by gluing together over a scheme, with the colocalization functors $\operatorname{Hom}_R(S,{-})$ used for the gluing (where $S$…

Given a perfect field of exponential characteristic $e$ and a functor $f:\mathcal A\to\mathcal B$ between symmetric monoidal strict $V$-categories of correspondences satisfying the cancellation property such that the induced morphisms of…