相关论文: A property of the interleaving distance for sheave…

Persistent homology has been recently studied with the tools of sheaf theory in the derived setting by Kashiwara and Schapira, after J. Curry has made the first link between persistent homology and sheaves. We prove the isometry theorem in…

The sheaf-function correspondence identifies the group of constructible functions on a real analytic manifold $M$ with the Grothendieck group of constructible sheaves on $M$. When $M$ is a finite dimensional real vector space,…

We interpret some results of persistent homology and barcodes (in any dimension) with the language of microlocal sheaf theory. For that purpose we study the derived category of sheaves on a real finite-dimensional vector space V. By using…

We prove uniform boundedness statements for semistable pure sheaves on projective manifolds. For example, we prove that the set of isomorphism classes of pure sheaves of dimension 2 that are slope semistable with respect to ample classes…

We show that for any constructible sheaf F on a smooth algebraic variety X over a field of arbitrary characteristic its singular support SS(F) is equidimensional of dimension dim X. Here SS(F) is the minimal closed subset of the cotangent…

We develop sheaf-theoretic methods to deal with non-smooth objects in symplectic geometry. We show the completeness of a derived category of sheaves with respect to the interleaving distance and construct a sheaf quantization of a…

Let $X$ be a smooth proper scheme over an algebraically closed field $k$ in characteristic $p$. In this short note, by interpreting $\mathcal{D}_{X}$-modules as $F$-divided sheaves and establishing a cohomological boundedness property for…

This thesis develops the theory of sheaves and cosheaves with an eye towards applications in science and engineering. To provide a theory that is computable, we focus on a combinatorial version of sheaves and cosheaves called cellular…

We present a uniform theory of constructible sheaves on arbitrary schemes with coefficients in topological or even condensed rings. This is accomplished by defining lisse sheaves to be the dualizable objects in the derived infinity-category…

In this paper we prove a duality for constructible sheaves on conically smooth stratified spaces. Here we consider sheaves with values in a stable and bicomplete $\infty$-category equipped with a closed symmetric monoidal structure, and in…

Building on Beilinson's work, ``constructible sheaves are holonomic,'' we introduce the notion of holonomicity for \'etale sheaves, without assuming a priori constructibility. Over a perfect base field, we establish the converse of…

Let S be a smooth projective surface, K be the canonical class of S and H be an ample divisor such that H.K<0 . In this paper we prove that for any rigid (Ext^1(F,F)=0) semistable sheaf F in the sense of Mumford--Takemoto stability w.r.t. H…

Let $X$ be a topologically stratified space, $p$ be any perversity on $X$, and $k$ be a field. We show that the category of $p$-perverse sheaves on $X$, constructible with respect to the stratification and with coefficients in $k$, is…

Let \(E\) be a finite-dimensional real vector space. We study invertible objects in the monoidal category of constructible sheaves on \(E\), endowed with the convolution product \(\star\). We show that the inverse of an invertible…

We introduce a notion of stability for sheaves with respect to several polarisations that generalises the usual notion of Gieseker-stability. We prove, under a boundedness assumption, which we show to hold on threefolds or for rank two…

We describe the compact objects in the $\infty$-category of $\mathcal C$-valued sheaves $\text{Shv} (X,\mathcal C)$ on a hypercomplete locally compact Hausdorff space $X$, for $\mathcal C$ a compactly generated stable $\infty$-category.…

When a non-singular complex projective surface $X$ satisfies that $K_X\sim 0$, we shall show that there are only finitely many isomorphic classes as abstract schemes in the set of moduli scheme of $H$-semistable sheaves with fixed Chern…

Let Z be a smooth projective manifold. In these notes I will prove that the K-group of R-constructible sheaves is isomorphic to the free abelian group with one generator for each open semialgebraic subset $U$ (which I will denote by the…

Let G be an algebraic group over an algebraically closed field, acting on a variety X with finitely many orbits. "Staggered sheaves" are certain complexes of G-equivariant coherent sheaves on X that seem to possess many remarkable…

We generalise the techniques of semistable reduction for flat families of sheaves to the setting of the derived category $D^b(X)$ of coherent sheaves on a smooth projective three-fold $X$. Then we construct the moduli of PT-semistable…