相关论文: Notes on Beilinson's "How to glue perverse sheaves…

We suggest a possibility for a categorical generalization of the concept of a perverse sheaf, in which vector spaces are replaced by triangulated categories. We call such hypothetical objects perverse Schobers and consider several examples,…

We study different notions of slope of a vector bundle over a smooth projective curve with respect to ampleness and affineness in order to apply this to tight closure problems. This method gives new degree estimates from above and from…

The Riemann-Hilbert correspondence embeds the triangulated category of (not necessarily regular) holonomic D-modules into that of $\mathbb R$-constructible enhanced ind-sheaves. The source category has a standard t-structure. Here, we…

In this paper, we construct recollements and ladders for exceptional curves by using reduction/insertion functors due to $p$-cycle construction. As applications to weighted projective lines, we classify recollements for the category of…

Sawin recently gave an axiomatic characterization of multiple Dirichlet series over the function field $\mathbb{F}_{q}(T)$ and proved their existence by exhibiting the coefficients as trace functions of specific perverse sheaves. However,…

We prove exactness of parabolic restriction and induction functors for conjugation equivariant sheaves on a reductive group generalizing a well known result of Lusztig who established this property for character sheaves. We propose a…

We conjecture that any perverse sheaf on a compact aspherical K\"ahler manifold has non-negative Euler characteristic. This extends the Singer-Hopf conjecture in the K\"ahler setting. We verify the stronger conjecture when the manifold X…

The purpose of this article is to set foundations for decomposition numbers of perverse sheaves, to give some methods to calculate them in simple cases, and to compute them concretely in two situations: for a simple (Kleinian) surface…

This article contains a proof of the basic lemma. This lemma, discovered by Beilinson, yields a motivic proof of the Andreotti-Frankel theorem for affine varieties. Next, it is shown that the category of Cohomologically Constructible…

Let A be an abelian group, not necessarily finite. The main objective of this paper is to provide two constructions for a fibered A-biset functor. The first is the lower plus construction, and the other is the upper plus construction. These…

We develop the theory of semi-orthogonal decompositions and spherical functors in the framework of stable $\infty$-categories. Building on this, we study the relative Waldhausen S-construction $S_\bullet(F)$ of a spherical functor $F$ and…

We introduce the notion of a holonomic D-module on a smooth (idealized) logarithmic scheme and show that Verdier duality can be extended to this context. In contrast to the classical case, the pushforward of a holonomic module along an open…

In a recent paper, M. Green and P. Griffiths used R. Thomas' works on nodal hypersurfaces to establish the equivalence of the Hodge conjecture and the existence of certain singular admissible normal functions. Inspired by their work, we…

We study the arithmetic Fourier transforms of trace functions on general connected commutative algebraic groups. To do so, we first prove a generic vanishing theorem for twists of perverse sheaves by characters, and using this tool, we…

Let X be a smooth, complete, geometrically connected curve over a field of characteristic p. The geometric Langlands conjecture states that to each irreducible rank n local system E on X one can attach a perverse sheaf on the moduli stack…

We show that the action of the Serre functor on the subcategory of projective-injective modules in a parabolic BGG category $\mathcal O$ of a quasi-reductive finite dimensional Lie superalgebra is given by tensoring with the top component…

In this article we study the perverse sheaf on Drinfeld's compactification obtained by applying the geometric Jacquet functor (alias nearby cycles) to a nondegenerate Whittaker sheaf. Namely, we describe its restrictions along the defect…

From descent theory to higher geometry, the idea of gluing has been embedded in many elegant and powerful techniques, proving instrumental for the solution of many problems. In this paper, we introduce a framework that allows to link…

On the complement $X= {\mathbb C}^2 - \bigcup_{i=1}^n L_i$ to a central plane line arrangement $\bigcup_{i=1}^n L_i \subset {\mathbb C}^2$, a locally constant sheaf of complex vector spaces $\mathcal L_a$ is associated to any multi-index $a…

We introduce a dynamical Mordell-Lang-type conjecture for coherent sheaves. When the sheaves are structure sheaves of closed subschemes, our conjecture becomes a statement about unlikely intersections. We prove an analogue of this…