Related papers: How to glue parity sheaves

Inspired by the works in linkage theory of modules, we define the concept of linkage of sheaves of modules as a generalization of linkage of modules. Thus, we expressed it in geometry algebraic language. We show that the linkedness of…

Our aim is to give a fairly complete account on the construction of compatible model structures on exact categories and symmetric monoidal exact categories, in some cases generalizing previously known results. We describe the close…

Let $R$ be a commutative ring with unit. We consider the homotopy theory of the category of spectral sequences of $R$-modules with the class of weak equivalences given by those morphisms inducing a quasi-isomorphism at a certain fixed page.…

We study the homotopy theory of locally ordered spaces, that is manifolds with boundary whose charts are partially ordered in a compatible way. Their category is not particularly well-behaved with respect to colimits. However, this category…

Let X be a proper scheme and Z a prestack over X equipped with a flat connection. We give a local-to-global description of D-modules on the prestack S(Z) of flat sections of Z. Examples of S(Z) include the moduli stacks of principal…

It is now very known how the subprojectivity of modules provides a fruitful new unified framework of the classical projectivity and flatness. In this paper, we extend this fact to the category of complexes by generalizing and unifying…

We introduce ``sheafification'' functors from categories of (lax monoidal) linear functors to categories of quasi-coherent sheaves (of algebras) of stacks. They generalize the homogeneous sheafification of graded modules for projective…

In this article we consider the homotopy theory of stratified spaces through a simplicial point of view. We first consider a model category of filtered simplicial sets over some fixed poset $P$, and show that it is a simplicial…

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…

We use the reflection group trick to glue manifolds with corners that are Borel-Serre compactifications of locally symmetric spaces of noncompact type and obtain aspherical manifolds. We call these \emph{piecewise locally symmetric}…

We display a symmetric monoidal equivalence between the stable $\infty$-category of filtered spectra, and quasi-coherent sheaves on $\mathbb{A}^1 / \mathbb{G}_m$, the quotient in the setting of spectral algebraic geometry, of the flat…

Homotopy links have proven to be one of the most powerful tools of stratified homotopy theory. In previous work, we described combinatorial models for the generalized homotopy links of a stratified simplicial set. For many purposes, in…

This is the first in a series of papers that deals with duality statements such as Mukai-duality (T-duality, from algebraic geometry) and the Baum-Connes conjecture (from operator $K$-theory). These dualities are expressed in terms of…

Let $\mathbb{k}$ be a field of characteristic $p$. We introduce a formalism of mixed sheaves with coefficients in $\mathbb{k}$ and showcase its use in representation theory. More precisely, we construct for all quasi-projective schemes $X$…

We give a formalism of mixed sheaves on varieties over a subfield of the complex number field.

We develop a theory of sheaves and cohomology on the category of proper modulus pairs. This complements [KMSY21], where a theory of sheaves and cohomology on the category of non-proper modulus pairs has been developed.

In this paper we show that states, transitions and behavior of concurrent systems can often be modeled as sheaves over a suitable topological space. In this context, geometric logic can be used to describe which local properties (i.e.…

Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…

We construct combinatorial model category structures on the categories of (marked) categories and (marked) pre-additive categories, and we characterize (marked) additive categories as fibrant objects in a Bousfield localization of…

In this paper, we try to realize the unbounded derived category of an abelian category as the homotopy category of a Quillen model structure on the category of unbounded chain complexes. We construct such a model structure based on…