Related papers: Regular holonomic D[[h]]-modules

In this paper, we will provide constructions of D-module structures on the complex computing the periodic cyclic homology of a stable infinity-category defined over a scheme of characteristic zero. We give two methods. The first one is…

We study relative and logarithmic characteristic cycles associated to holonomic $\mathscr D$-modules. As applications, we obtain: (1) an alternative proof of Ginsburg's log characteristic cycle formula for lattices of regular holonomic…

This paper grew out of the author's work on arXiv:2504.18460. Differential operators in the sense of Grothendieck acting between modules over a commutative ring can be interpreted as torsion elements in the bimodule of all operators with…

A differential module is a module equipped with a square-zero endomorphism. This structure underpins complexes of modules over rings, as well as differential graded modules over graded rings. We establish lower bounds on the class--a…

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 compute formal invariants associated with the cohomology sheaves of the direct image of holonomic D-modules of exponential type. We also prove that every formal C[[t]]<\partial_t>-modules is isomorphic, after a ramification, to a germ of…

A holonomic D-module on a complex analytic manifoldadmits always a b-function along any submanifold. If the module is regular, itadmits also a regular b-function, that is a b-function with a condition on the order of the lower terms of the…

We formulate and prove a Riemann--Hilbert correspondence between two categories: wild difference modules and wild Stokes-filtered $\mathscr{A}_{\rm{per}}$-modules. This correspondence is motivated by the Riemann--Hilbert correspondence for…

We present a non-perturbative formulation of renormalization by viewing the regularized Schwinger-Dyson hierarchy as a meromorphic connection, that is, as a D-module on the product of spacetime with the regulator disc. The irregular…

We present an algorithm to construct a basis of k-th extension group of a D-module M in ring of the formal power series Ext_D^k(M,O).

Let $\mathcal{H}$ be a Hilbert space, and let $K(\mathcal{H})$ be the $C^*$-algebra of compact operators on $\mathcal{H}$. In this paper, we present some characterizations of the norm-parallelism for elements of a Hilbert…

We construct explicitly noncommutative deformations of categories of holomorphic line bundles over higher dimensional tori. Our basic tools are Heisenberg modules over noncommutative tori and complex/holomorphic structures on them…

We study the categories of discrete modules for topological rings arising as the rings of operations in various kinds of topological K-theory. We prove that for these rings the discrete modules coincide with those modules which are locally…

Beilinson--Bernstein localisation relates representations of a Lie algebra $\mathfrak{g}$ to certain $\mathcal{D}$-modules on the flag variety of $\mathfrak{g}$. In [arXiv:2002.01540], examples of $\mathfrak{sl}_2$-representations which…

In this note we show that the holonomies for higher local systems provided by the higher Riemann-Hilbert correspondence coincide with those associated to principal $2$-bundles where both formalisms meet.

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…

The general framework for integrable discrete systems on R in particular containing lattice soliton systems and their q-deformed analogues is presented. The concept of regular grain structures on R, generated by discrete one-parameter…

We prove that, on a Riemann surface, the functor $\mathrm{RH}^S$ constructed in a previous work as a right quasi-inverse of the solution functor from the bounded derived category of regular relative holonomic modules to that of relative…

We undertake the study of bivariate Horn systems for generic parameters. We prove that these hypergeometric systems are holonomic, and we provide an explicit formula for their holonomic rank as well as bases of their spaces of complex…

The aim of this note is to prove various general properties of a generalization of the full module of first order differential operators on a commutative ring - a $\operatorname{D}$-Lie algebra. A $\operatorname{D}$-Lie algebra $\tilde{L}$…