Related papers: The de Rham functor for logarithmic D-modules

On a complex manifold, the embedding of the category of regular holonomic D-modules into that of holonomic D-modules has a left quasi-inverse functor $\mathcal{M}\mapsto\mathcal{M}_{\mathrm{reg}}$, called regularization. Recall that…

We calculate the category of D-modules on the loop space of the affine line in coherent terms. Specifically, we find that this category is derived equivalent to the category of ind-coherent sheaves on the moduli space of rank one de Rham…

Let $X$ be a complex analytic manifold, $D\subset X$ a locally quasi-homogeneous free divisor, $E$ an integrable logarithmic connection with respect to $D$ and $L$ the local system of the horizontal sections of $E$ on $X-D$. In this paper…

Given an effective Cartier divisor D with simple normal crossing support on a smooth and proper scheme X over a perfect field of positive characteristic p, there is a natural notion of de Rham-Witt sheaves on X with zeros along D. We show…

We will prove a Kodaira-Nakano type of vanishing theorem for the logarithmic de Rham complex of unitary local system. We will then study the weight filtration on the logarithmic de Rham complex, and prove a stronger statement for the…

In this paper, we study the holonomic $D$-modules when $D$ is the ring of $k$-linear differential operators on $A = k[\Gamma]$, the coordinate ring of an affine monomial curve over the complex numbers $k = \mathbb C$. In particular, we…

In D-module theory, we have the notion of the restriction of a module along a smooth variety. T. Oaku and N. Takayama have described a process to compute the restriction, which starts from a free resolution adapted to the V-filtration of…

We study holomorphic foliations on normal crossings varieties arising as semistable degenerations. We do so by we exploring the notion of foliated d-semistability using the language of logarithmic structures in the sense of…

We construct a moduli scheme for semistable pre-$\D$-modules with prescribed singularities and numerical data on a smooth projective variety. These pre-$\D$-modules are to be viewed as regular holonomic $\D$-modules with `level structure'.…

We study log D-modules on smooth log pairs and construct a comparison theorem of log de Rham complexes. The proof uses Sabbah's generalized b-functions. As applications, we deduce a log index theorem and a Riemann-Roch type formula for…

This paper is a contribution to the study of relative holonomic $\mathcal{D}$-modules. Contrary to the absolute case, the standard $t$-structure on holonomic $\mathcal{D}$-modules is not preserved by duality and hence the solution functor…

We study some aspects of conjugation and descent in the context of the irregular Riemann-Hilbert correspondence of D'Agnolo-Kashiwara. First, we give a proof of the fact that Kashiwara's conjugation functor for holonomic D-modules is…

We study the category of holonomic $\mathscr{D}_{X}$-modules for a quasi-compact, quasi-separated, smooth rigid analytic variety $X$ over the field $\mathbb{C}(\!(t)\!)$. In particular, we prove finiteness of the de Rham cohomology for such…

In this paper we introduce a generalization of the Nakayama functor for finite-dimensional algebras. This is obtained by abstracting its interaction with the forgetful functor to vector spaces. In particular, we characterize the Nakayama…

Let $X$ and $S$ be complex analytic manifolds where $S$ plays the role of a parameter space. Using the sheaf $\DXS^{\infty}$ of relative differential operators of infinite order, we construct functorially the regular holonomic $\DXS$-module…

We compute the characters of the simple GL-equivariant holonomic D-modules on the vector spaces of general, symmetric and skew-symmetric matrices. We realize some of these D-modules explicitly as subquotients in the pole order filtration…

Let X be a complex analytic manifold and D \subset X a free divisor. Integrable logarithmic connections along D can be seen as locally free {\cal O}_X-modules endowed with a (left) module structure over the ring of logarithmic differential…

We prove a structure theorem for the differential operator in the 0-term of the ${\cal V}$-filtration with respect to a free divisor. Using this theorem, we give a formula for the logarithmic de Rham complex in terms of ${\cal…

We obtain Morita invariant versions of Eilenberg-Watts type theorems, relating Deligne products of finite linear categories to categories of left exact as well as of right exact functors. This makes it possible to switch between different…

We compute the moduli of endomorphisms of the de Rham and crystalline cohomology functors, viewed as a cohomology theory on smooth schemes over truncated Witt vectors. As applications of our result, we deduce Drinfeld's refinement of the…