Related papers: The six operations in topology

We study the unwrapped Fukaya category of Lagrangian branes ending on a Legendrian knot. Our knots live at contact infinity in the cotangent bundle of a surface, the Fukaya category of which is equivalent to the category of constructible…

Let S be a Noetherian scheme and f:X -> S a proper morphism. By SGA 4 XIV, for any constructible sheaf F of Z/nZ-modules on X, the sheaves of Z/nZ-modules R^if_*F obtained by direct image (for the etale topology) are also constructible:…

We lay out an infinity categorical interpretation of reconstruction theorems which are germane to the symmetric monoidal perspective of noncommutative algebraic geometry, present sufficient conditions which allow for the factorization of…

This article aims to provide a novel formalization of the concept of computational irreducibility in terms of the exactness of functorial correspondence between a category of data structures and elementary computations and a corresponding…

This paper explores the sheaves with the action of a lie algebra and computes their cohomology in a new category. Then in the following sections, We try to generalize a classical result in [GM, Ch. IV] about exterior algebra. We add the…

We develop a microlocal theory, in the sense of Kashiwara-Schapira, for Zariski-constructible sheaves on rigid analytic varieties. We define and study monodromic sheaves, the monodromic Fourier transform, specialisation, microlocalisation,…

We arrange morphisms and comorphisms of sites as the horizontal and vertical cells of a double category of sites; using the formalism of extensions and restrictions of presheaves, we explains how one can define a sheafification double…

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…

Given an open-closed decomposition of the stratifying poset, we construct a new semi-orthogonal decomposition of the $\infty$-category of constructible sheaves on a stratified space admitting an exit-path $\infty$-category. From this we…

We prove the surprising fact that the infinity-category of stabilized Liouville sectors is a localization of an ordinary category of stabilized Liouville sectors and strict sectorial embeddings. From the perspective of homotopy theory, this…

We give explicit formulas for the local multiplicative convolution functors which express the local monodromies of the convolution of two $\ell$-adic sheaves on the torus ${\mathbb G}_m$ over the algebraic closure of a finite field in terms…

In this article, it is shown that derivator six-functor-formalisms on any (classical) site canonically extend to higher geometric stacks as defined by To\"en-Vezzosi under some natural locality conditions. As an application, it is shown…

After the universal property of the six functor formalism $\Shv(-;\Sp)$ on locally compact Hausdorff spaces given by Zhu, we show that the six functor formalism $\Shv(-;\Sp)$ on light condensed anima in the sense of Heyer-Mann is initial…

This paper shows that generalizations of operads equipped with their respective bar/cobar dualities are related by a six operations formalism analogous to that of classical contexts in algebraic geometry. As a consequence of our…

We investigate conditions for the extendibility of continuous algebra homomorphisms $\phi$ from the Fourier algebra $A(F)$ of a locally compact group $F$ to the Fourier-Stieltjes algebra $B(G)$ of a locally compact group $G$ to maps between…

Local scaling of a set means that in a neighborhood of a point the structure of the set can be mapped into a finer scale structure of the set. These scaling transformations are compact sets of locally affine (that is: with uniformly…

We study sheaves in the context of a duality theory for lattice structure endowed with extra operations, and in the context of forcing in a topos. Using Sheaf duality theory of Comer for cylindric algebras, we give a representation theorem…

Given a generically \'etale morphism $f\colon Y\to X$ of quasi-smooth Berkovich curves, we define a different function $\delta_f\colon Y\to[0,1]$ that measures the wildness of the topological ramification locus of $f$. This provides a new…

We prove that the semigroup operation of a topological semigroup $S$ extends to a continuous semigroup operation on its the Stone-\v{C}ech compactification $\beta S$ provided $S$ is a pseudocompact openly factorizable space, which means…

On a smooth algebraic variety over $\mathbb{C}$, we build the tempered subanalytic and Stein tempered subanalytic sites. We construct the sheaf of holomorphic functions tempered at infinity over these sites and study their relations with…