Related papers: Log D-modules and Index theorems

Kashiwara conjectured that the hard Lefshetz theorem and the semisimplicity theorem hold for any semisimple perverse sheaf M on a variety over a field of characteristic 0. He also conjectured that if you apply to such M the nearby cycle…

We describe a noncommutative deformation theory for presheaves and sheaves of modules that generalizes the commutative deformation theory of these global algebraic structures, and the noncommutative deformation theory of modules over…

We classify contravariant pairings between standard Whittaker modules and Verma modules over a complex semisimple Lie algebra. These contravariant pairings are useful in extending several classical techniques for category $\mathcal{O}$ to…

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…

We exhibit a relationship between projective duality and the sheaf of logarithmic vector fields along a reduced divisor $D$ of projective space, in that the push-forward of the ideal sheaf of the conormal variety in the point-hyperplane…

We prove the decomposition theorem for Hodge modules with integral structure along proper K\"ahler morphisms, partially generalizing M. Saito's theorem for projective morphisms. Our proof relies on compactifications of period maps of…

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…

The aim of this note is threefold. The first is to obtain a simple characterization of relative constructible sheaves when the parameter space is projective. The second is to study the relative Fourier-Mukai for relative constructible…

The purpose of this survey is to present analytic versions of the injectivity theorem and their applications. The proof of our injectivity theorems is based on a combination of the L^2-method for the dbar-equation and the theory of harmonic…

We introduce the notion of idempotent radical class of module coalgebras over a bialgebra B. We prove that if R is an idempotent radical class of B-module coalgebras, then every B-module coalgebra contains a unique maximal B-submodule…

We consider a smooth groupoid of the form \Sigma\rtimes\Gamma where \Sigma is a Riemann surface and \Gamma a discrete pseudogroup acting on \Sigma by local conformal diffeomorphisms. After defining a K-cycle on the crossed product…

We prove an Induction Equivalence and a Kashiwara Equivalence for coadmissible equivariant D-modules on rigid analytic spaces. This allows us to completely classify such objects with support in a single orbit of a classical point with…

In this paper, we study the cohomology of semisimple local systems in the spirit of classical Hodge theory. On the one hand, we establish a generalization of Hodge-Riemann bilinear relations. For a semisimple local system on a smooth…

We generalize the functorial quasi-isomorphism in \cite{Davis2011} from overconvergent Witt de-Rham cohomology to rigid cohomology on smooth varieties over a finite field $k$, dropping the quasi-projectiveness condition. We do so by…

Fabian Januszewski and the author established the theory of twisted D-modules over general base schemes. In this short note, we construct a $K$-invariant positive exhaustive filtration on the globalization of the twisted D-module on a…

For a morphism of smooth schemes over a regular affine base we define functors of derived direct image and extraordinary inverse image on coderived categories of DG-modules over de Rham DG-algebras. Positselski proved that for a smooth…

The universal Spencer and de Rham complexes of sheaves over a smooth or analytical manifold are well known to play a basic role in the theory of $\mathcal{D}$-modules. In this article we consider a double complex of sheaves generalizing…

Building on the theory of parity sheaves due to Juteau-Mautner-Williamson, we develop a formalism of "mixed modular perverse sheaves" for varieties equipped with a stratification by affine spaces. We then give two applications: (1) a…

For a reductive group $G$, Harder-Narasimhan theory gives a structure theorem for principal $G$ bundles on a smooth projective curve $C$. A bundle is either semistable, or it admits a canonical parabolic reduction whose associated Levi…

We study twisted D-modules on the weighted projective stacks. We determine for which values of the twist and the weight the global section functor is an equivalence, thus, proving a version of Beilinson-Bernstein Localisation Theorem.