Related papers: Characteristic cycle and wild Lefschetz theorems

Recently, the singular support and the characteristic cycle of an \'etale sheaf on a smooth variety over a perfect field are constructed by Beilinson and Saito, respectively. In this article, we extend the singular support to a relative…

We define the characteristic cycle of an etale sheaf as a cycle on the cotangent bundle of a smooth variety in positive characteristic using the singular support recently defined by Beilinson. We prove a formula a la Milnor for the total…

We prove a characteristic p analogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain intersection multiplicities of the characteristic cycle of that sheaf. This uses the construction…

We give a short and self-contained proof of the Decomposition Theorem for the non-small resolution of a Special Schubert variety. We also provide an explicit description of the perverse cohomology sheaves. As a by-product of our approach,…

We introduce a new fundamental group scheme for varieties defined over an algebraically closed field of positive characteristic and we use it to study generalization of some of C. Simpson's results to positive characteristic. We also study…

We propose a point of view on resurgence theory based on the study of perverse sheaves on the complex line carrying an algebraic structure with respect to additive convolution. In particular, we lift the concept of alien derivatives…

This paper is an introduction to the use of perverse sheaves with positive characteristic coefficients in modular representation theory. In the first part, we survey results relating singularities in finite and affine Schubert varieties and…

We prove the hard Lefschetz property for pseudomanifolds and cycles in any characteristic with respect to an appropriate Artinian reduction. The proof is a combination of Adiprasito's biased pairing theory and a generalization of a formula…

The goal of this paper is to explain how basic properties of perverse sheaves sometimes translate via Riemann-Hilbert correspondences (in both characteristic $0$ and characteristic $p$) to highly non-trivial properties of singularities,…

We give a motivated introduction to the theory of perverse sheaves, culminating in the Decomposition Theorem of Beilinson, Bernstein, Deligne and Gabber. A goal of this survey is to show how the theory develops naturally from classical…

Revised: just some typos, reorganized a bit the article. It will be published in the VIASM Annual meeting, Hanoi. We give a detailed account of Deligne's letter to Drinfeld dated June 18, 2011, in which he shows that there are finitely many…

We prove that character sheaves have nilpotent singular support in any characteristic, partially extending the work of Mirkovic, Vilonen and independently Ginzburg to positive characteristic. We do this by introducing a category of tame…

We prove that for extended Dynkin quivers, simple perverse sheaves in Lusztig category are characterized by the nilpotency of their singular support. This proves a conjecture of Lusztig in the case of affine quivers. For cyclic quivers, we…

Let $G$ be a connected reductive group over $F_q$, where $q$ is large enough and the center of $G$ is connected. We are concerned with Lusztig's theory of {\em character sheaves}, a geometric version of the classical character theory of the…

We prove an extended Lefschetz principle for a large class of pencils of hypersurfaces having isolated singularities, possibly in the axis, and show that the module of vanishing cycles is generated by the images of certain variation maps.

Over a connected geometrically unibranch scheme $X$ of finite type over a finite field, we show finiteness of the number of irreducible $\bar \Q_\ell$-lisse sheaves, with bounded rank and bounded ramification in the sense of Drinfeld, up to…

We count points over a finite field on wild character varieties of Riemann surfaces for singularities with regular semisimple leading term. The new feature in our counting formulas is the appearance of characters of Yokonuma-Hecke algebras.…

We formulate a conjectural hard Lefschetz property for Chow groups, and prove this in some special cases: roughly speaking, for varieties with finite-dimensional motive, and for varieties whose self-product has vanishing middle-dimensional…

In this note, we study the infinitesimal forms of Deligne cycle class maps. As an application, we prove that the infinitesimal form of a conjecture by Beilinson is true.

We analyze irreducible perverse sheaves on abelian varieties, defined over the complex numbers or the algebraic closure of a finite field, whose Euler characteristic is zero. We give a description of such perverse sheaves under assumptions…