Related papers: A note on linear stacks

This is the second of series of papers on the study of foliations in the setting of derived algebraic geometry based on the central notion of derived foliation. We introduce sheaf-like coefficients for derived foliations, called…

An abstract theory of ultradifferentiable sheafs is developed. Moreover, various applications to the theory of linear partial differential equations, differential geometry and, in particular, CR geometry are discussed.

These are notes on derived algebraic geometry in the context of animated rings. More precisely, we recall the proof of To\"en-Vaqui\'e that the derived stack of perfect complexes is locally geometric in the language of $\infty$-categories.…

In this paper, we expand the foundations of derived complex analytic geometry introduced in [DAG-IX] by J. Lurie. We start by studying the analytification functor and its properties. In particular, we prove that for a derived complex scheme…

This article presents a continuous model for hierarchical networks based on a combination of mathematically derived models of receptive fields and biologically inspired computations. Based on a functional model of complex cells in terms of…

The goal of this paper is to show that Stokes data coming from flat bundles form a locally geometric derived stack locally of finite presentation. This generalizes existing geometricity results on Stokes data in four different directions:…

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…

This work focuses on approximation and generation for the derived category of complexes with quasi-coherent cohomology on algebraic stacks. Our methods establish that approximation by compact objects descends along covers that are…

This paper provides an overview of the applications of sheaf theory in deep learning, data science, and computer science in general. The primary text of this work serves as a friendly introduction to applied and computational sheaf theory…

In this paper, we consider linear elliptic systems from composite materials where the coefficients depend on the shape and might have the discontinuity between the subregions. We derive a function which is related to the gradient of the…

We define graded, quasi-coherent $\mathcal{O}_S$-algebras over a given base derived scheme $S$, and show that these are equivalent to derived $\mathbb{G}_{m,S}$-schemes which are affine over $S$. We then use this $\mathbb{G}_{m,S}$-action…

We give an alternate formulation of pseudo-coherence over an arbitrary derived stack X. The full subcategory of pseudo-coherent objects forms a stable sub-infinity-category of the derived category associated to X. Using relative…

In these notes, an introduction to derived categories and derived functors is given. The main focus is the bounded derived category of coherent sheaves on a smooth projective variety.

In arXiv:1807.09038 we formulated a conjecture describing the derived category D-mod(Gr$_{GL(n)}$) of (all) D-modules on the affine Grassmannian of the group $GL(n)$ as the category of quasi-coherent sheaves on a certain stack (it is…

We define a derived enhancement of the hyperquot scheme (also known as nested Quot scheme), which classically parametrises flags of quotients of a perfect coherent sheaf on a projective scheme. We prove it is representable by a derived…

We construct a fully-faithful functor of $\infty$-categories from complexes of D-cap modules with Fr\'echet cohomology to quasi-coherent sheaves on an analytic stack. We prove various descent results for $\infty$-categories of D-cap modules…

In order to develop the foundations of logarithmic derived geometry, we introduce a model category of logarithmic simplicial rings and a notion of derived log \'etale maps and use this to define derived log stacks.

Fix a scheme $X$ over a field of characteristic zero that is equipped with an action of a reductive algebraic group $G$. We give necessary and sufficient conditions for a $G$-equivariant coherent sheaf on $X$ or a bounded-above complex of…

In the paper we answer the following question: for a morphism of varieties (or, more generally, stacks), when the derived category of the base can be recovered from the derived category of the covering variety by means of descent theory? As…

We build an infinite dimensional scheme parametrizing isomorphism classes of coherent quotients of a quasi-coherent sheaf on a projective scheme. The main tool to achieve the construction is a version of Grothendieck's Grassmannian…