Related papers: Localizing invariants of constructible sheaves

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…

This note is a part of the lecture notes of a graduate student algebraic geometry seminar held at the department of mathematics in National Taiwan Normal University, 2020 Falls. It aims to introduce an example of sheaves defined on posets…

We confirm the quasi-projective case of Saito's conjecture, namely that the cohomological characteristic classes defined by Abbes and Saito can be computed in terms of the characteristic cycles. We construct a cohomological characteristic…

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…

It is usually not straightforward to work with the category of perverse sheaves on a variety using only its definition as a heart of a $t$-structure. In this paper, the category of perverse sheaves on a smooth toric variety with its orbit…

We use the theory of dual of Fr\'echet-Schwartz (DFS) spaces to establish a sufficient condition for top-degree solvability for the differential complex associated to a hypocomplex locally integrable structure. As an application, we show…

In the framework of Abstract Differential Geometry, we show that to a given principal sheaf and a representation of its stuctural sheaf in $A^n$, where A is a sheaf of associative, commutative, unital algebras (over R or C), we associate a…

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More generally, the same assertion holds for any countably…

Let $p$ be a prime number and let $X$ be a complex algebraic variety with an action of $\mathbb{Z}/p\mathbb{Z}$. We develop the theory of parity complexes in a certain $2$-periodic localization of the equivariant constructible derived…

Let $X$ be any rational surface. We construct a tilting bundle $T$ on $X$. Moreover, we can choose $T$ in such way that its endomorphism algebra is quasi-hereditary. In particular, the bounded derived category of coherent sheaves on $X$ is…

We construct a rational homotopy pullback decomposition for variants of the classifying space of the group of homeomorphisms for a large class of manifolds. This has various applications, including a rational section of the stabilisation…

In this paper we introduce constructible analogs of the discrete complexity classes $\mathbf{VP}$ and $\mathbf{VNP}$ of sequences of functions. The functions in the new definitions are constructible functions on $\mathbb{R}^n$ or…

For a normal variety X defined over an algebraically closed field with an action of the multiplicative group G_m, we consider the ``hyperbolic localization'' functor from D^b(X) to D^b(X^T), which localizes using closed supports in the…

We give an account of Bousfield localisation and colocalisation for one-dimensional model categories---ones enriched over the model category of $0$-types. A distinguishing feature of our treatment is that it builds localisations and…

Let $\Bbbk$ be an algebraically closed field of characteristic zero. Let $\mathrm{Sch}/\Bbbk$ denote the category of schemes of finite type over $\Bbbk$. Let $B$ be a connected projective scheme over $\Bbbk$ and let $\mathcal L$ be an ample…

Given a nontrivial semi-orthogonal decomposition $\Perf(\X)=\langle \mathcal{A},\mathcal{B}\rangle$, and assume that the base locus of $\omega_{\X}$ is a proper closed subset, it was proved by Kotaro Kawatani and Shinnosuke Okawa that all…

We describe and prove correctness of two practical algorithms for finding indecomposable summands of finitely generated modules over a finitely generated k-algebra R. The first algorithm applies in the (multi)graded case, which enables the…

We construct natural equivalences between derived categories of coherent sheaves on the local models for stratified Mukai or Atiyah flops (of type A).

Consider a family of integral complex locally planar curves. We show that under some assumptions on the basis, the relative nested Hilbert scheme is smooth. In this case, the decomposition theorem of Beilinson, Bernstein and Deligne asserts…

We give sufficient conditions for the affinity of Etingof's sheaves of Cherednik algebras on projective space. To do this we introduce the notion of pull-back of modules under certain flat morphisms.