Related papers: Graded Holonomic D-modules on Monomial Curves

We present a method to compute the holonomic extension of a $D$-module from a Zariski open set in affine space to the whole space. A particular application is the localization of coherent $D$-modules which are holonomic on the complement of…

We study Fourier transforms of regular holonomic D-modules. In particular we show that their solution complexes are monodromic. An application to direct images of some irregular holonomic D-modules will be given. Moreover we give a new…

We study the ring of differential operators D(X) on the basic affine space X=G/U of a complex semisimple group G with maximal unipotent subgroup U. One of the main results shows that the cohomology group H^*(X,O_X) decomposes as a finite…

The aim of the present paper is to study arithmetic properties of $\mathcal{D}$-modules on an algebraic variety over the field of algebraic numbers. We first provide a framework for extending a class of $G$-connections (resp., globally…

Let A denote the ring of differential operators on the affine line with its two usual generators t and d/dt given degrees +1 and -1 respectively. Let X be the stack having coarse moduli space the affine line Spec k[z] and isotropy groups…

Let $I \subset R = \mathbb{F}[x_1,x_2]$ be a height two ideal minimally generated by three homogeneous polynomials of the same degree $d$, where $\mathbb{F}$ is a field of characteristic zero. We use the theory of $D$-modules to deduce…

Given a grading on a nonassociative algebra by an abelian group, we have two subgroups of automorphisms attached to it: the automorphisms that stabilize each homogeneous component (as a subspace) and the automorphisms that permute the…

Let $K$ be a field of characteristic zero, $R = K[X_1,\ldots,X_n]$. Let $A_n(K) = K<X_1,\ldots,X_n, \partial_1, \ldots, \partial_n>$ be the $n^{th}$ Weyl algebra over $K$. We consider the case when $R$ and $A_n(K)$ is graded by giving $\deg…

Let A be a finitely generated connected graded k-algebra defined by a finite number of monomial relations. Then there is a finite directed graph, Q, the Ufnarovskii graph of A, for which the categories QGr(A) and QGr(kQ) are equivalent:…

Let $K$ be a field of characteristic zero, $R = K[X_1,...,X_n]$. Let $A_n(K) = K<X_1,...,X_n, \partial_1, ..., \partial_n>$ be the $n^{th}$ Weyl algebra over $K$. We consider the case when $R$ and $A_n(K)$ is graded by giving $\deg X_i =…

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…

The aim of this paper is to study in details the regular holonomic $D-$module introduced in \cite{[B.19]} whose local solutions outside the polar hyper-surface $\{\Delta(\sigma).\sigma_k = 0 \}$ are given by the local system generated by…

Let $R = k[x_1, \ldots, x_n]$ be a polynomial ring over a field $k$ of characteristic zero and $\cR$ be the formal power series ring $k[[x_1, \ldots, x_n]]$. If $M$ is a $\D$-module over $R$, then $\cR \otimes_R M$ is naturally a…

Given a grading $\Gamma: A=\oplus_{g\in G}A_g$ on a nonassociative algebra $A$ by an abelian group $G$, we have two subgroups of the group of automorphisms of $A$: the automorphisms that stabilize each homogeneous component $A_g$ (as a…

Consider $(G, V)$ a finite-dimensional representation of a connected reductive complex Lie group $G$ and $\mathbb{P}\left( V\right) $ the projective space of $V$. Denote by $G'$ the derived subgroup of $G$ and assume that the categorical…

Let V be a finite dimensional representation of the connected complex reductive group H. Denote by G the derived subgroup of H and assume that the categorical quotient of V by G is one dimensional. In this situation there exists a…

We compute, by D-module restrictions, the slopes of irregular hypergeometric systems associated to a monomial curve.

Given a grading by an abelian group G on a semisimple Lie algebra L over an algebraically closed field of characteristic 0, we classify up to isomorphism the simple objects in the category of finite-dimensional G-graded L-modules. The…

Let \Y be a derived algebraic stack satisfying some mild conditions. The purpose of this paper is three-fold. First, we introduce and study H(\Y), a monoidal DG category that might be regarded as a categorification of the ring of…

Differential modules over a commutative differential ring R which are finitely generated projective as ring modules, with differential homomorphisms, form an additive category, so their isomorphism classes form a monoid. We study the…