Related papers: The NilHecke schober

We show a surprising link between singularity theory and the invariant subspace problem of nilpotent operators as recently studied by C. M. Ringel and M. Schmidmeier, a problem with a longstanding history going back to G. Birkhoff. The link…

We define a stratification of the moduli stack of coherent sheaves on an elliptic curve which allows us (1) to give an explicit description of the irreducible components of the global nilpotent cone of elliptic curves, (2) to establish an…

We propose an abelian categorification of $\hat{Z}$-invariants for Seifert $3$-manifolds. First, we give a recursive combinatorial derivation of these $\hat{Z}$-invariants using graphs with certain hypercubic structures. Next, we consider…

Using a geometric argument building on our new theory of graded sheaves, we compute the categorical trace and Drinfel'd center of the (graded) finite Hecke category $\mathsf{H}_W^\mathsf{gr} = \mathsf{Ch}^b(\mathsf{SBim}_W)$ in terms of the…

Tannaka duality and its extensions by Lurie, Sch\"appi et al. reveal that many schemes as well as algebraic stacks may be identified with their tensor categories of quasi-coherent sheaves. In this thesis we study constructions of cocomplete…

We describe the equivariant cohomology of cofibers of spherical perverse sheaves on the affine Grassmannian of a reductive algebraic group in terms of the geometry of the Langlands dual group. In fact we give two equivalent descriptions:…

In the first section we study a functor of Bezrukavnikov, Finkelberg and Ostrik defined on character sheaves; we compute it in a Grothendieck group taking weights into account. In the second section we enlarge the class of character sheaves…

Let K be the field of fractions of a Henselian discrete valuation ring O_K. Let X_K/K be a smooth proper geometrically connected scheme admitting a regular model X/O_K. We show that the index \delta(X_K/K) of X_K/K can be explicitly…

This article can be seen as a sequel to the first author's article ``Chern classes of the tangent bundle on the Hilbert scheme of points on the affine plane'', where he calculates the total Chern class of the Hilbert schemes of points on…

We develop an invariant deformation theory, in a form accessible to practice, for affine schemes $W$ equipped with an action of a reductive algebraic group $G$. Given the defining equations of a $G$-invariant subscheme $X \subset W$, we…

In this paper, we are interested in the construction of a bilinear pseudodifferential calculus. We define some symbolic classes which contains those of Coifman-Meyer. These new classes allow us to consider operators closely related to the…

If $X$ is a variety over a number field, Annette Huber has defined a category of "horizontal" (or "almost everywhere unramified") $\ell$-adic complexes and $\ell$-adic perverse sheaves on $X$. For such objects, the notion of weights makes…

Let Q be an affine quiver of type A. Let C be the associated generalized Cartan matrix. Let U^- be the negative part of the quantized enveloping algebra attached to C. In terms of perverse sheaves on the moduli space of representations of a…

For a large class of geometric objects, the passage to categories of quasi-coherent sheaves provides an embedding in the 2-category of abelian tensor categories. The notion of weakly Tannakian categories introduced by the author gives a…

We consider a class of relative $n$-Calabi--Yau dg-algebras, referred to as relative Ginzburg algebras, associated with marked surfaces equipped with a decomposition into $n$-gons ($n$-angulation). We relate their derived categories to the…

We prove a conjecture of Frenkel, Gaitsgory, Kazhdan and Vilonen, related to Fourier coefficients of spherical perverse sheaves on the affine Grassmannian associated to a a split reductive group. Our proof is an extension of the proof given…

We study quantizations of transverse slices to Schubert varieties in the affine Grassmannian. The quantization is constructed using quantum groups called shifted Yangians --- these are subalgebras of the Yangian we introduce which…

Let X be a compact complex manifold, $D_c^b(X)$ be the bounded derived category of constructible sheaves on $X$, and $Fuk(T^*X)$ be the Fukaya category of $T^*X$. A Lagrangian brane in $Fuk(T^*X)$ is holomorphic if the underlying Lagrangian…

In arXiv:0805.0157v5, the authors define a class of derived stacks, called "perfect stacks" and show that for this class the categories of quasi-coherent sheaves satisfy a categorical K\"unneth formula. Motivated to extend their results to…

We give a presentation of localized affine and degenerate affine Hecke algebras of arbitrary type in terms of weights of the polynomial subalgebra and varied Demazure-BGG type operators. We offer a definition of a graded algebra…