Related papers: On the V-filtration of D-modules

We determine the irregular Hodge filtration, as introduced by Sabbah, for the purely irregular hypergeometric $\mathcal{D}$-modules. We obtain in particular a formula for the irregular Hodge numbers of these systems. We use the reduction of…

In this work we extend the concept of the Lipschitz saturation of an ideal defined in [5] to the context of modules in some different ways, and we prove they are generically equivalent.

We compute the Jantzen filtration of a D-module on the flag variety of $\mathrm{SL}_2(\mathbb{C})$. At each step in the computation, we illustrate the $\mathfrak{sl}_2(\mathbb{C})$-module structure on global sections to give an algebraic…

This work reports on joint research with Manuel Saorin. For an algebra A over an algebraically closed field k the set of A-module structures on k d forms an affine algebraic variety. The general linear group Gl d (k) acts on this variety…

We investigate infinite dimensional modules for an affine group scheme $\mathbb G$ of finite type over a field of positive characteristic $p$. For any subspace $X \subset \mathcal O(\mathbb G)$ of the coordinate algebra of $\mathbb G$, we…

By any measure, semisimple modules form one of the most important classes of modules and play a distinguished role in the module theory and its applications. One of the most fundamental results in this area is the Wedderburn-Artin theorem.…

Consider a complex analytic manifold $X$ and a coherent Lie subalgebra $\shi$ of the Lie algebra of complex vector fields on $X$. By using a natural $\shd_X$-module $\shm_\shi$ naturally associated to $\shi$ and the ring (in the derived…

With the aid of the exponentiation functor and Fourier transform we introduce a class of modules $T(g,V,S)$ of $\mathfrak{sl} (n+1)$ of mixed tensor type. By varying the polynomial $g$, the $\mathfrak{gl}(n)$-module $V$, and the set $S$, we…

The aim of this article is twofold: first, improve the multiplicity estimate obtained by the second author for Drinfeld quasi-modular forms; and then, study the structure of certain algebras of "almost-$A$-quasi-modular forms"

We introduce and study certain deformations of Drinfeld quasi-modular forms by using rigid analytic trivialisations of corresponding Anderson's t-motives. We show that a sub-algebra of these deformations has a natural graduation by the…

We extend the deformation theory algorithm of matrix factorizations to systems with more than one D-brane. The obstructions to the deformations are F-term equations which can be integrated to an effective superpotential. We demonstrate the…

We introduce the notion of a favourable module for a complex unipotent algebraic group, whose properties are governed by the combinatorics of an associated polytope. We describe two filtrations of the module, one given by the total degree…

By building on a method introduced by Kashiwara and refined by Lichtin, we give upper bounds for the roots of certain b-functions associated to a regular function f in terms of a log resolution of singularities. As applications, we recover…

Let R be a polynomial ring over k(u), where k is a field k and u is a finite family or inderterminates. The paper introduces the specialization of an arbitrary finitely generated R-module by the substitution of u to elements of k. This…

These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.

Let $R$ be a commutative unital ring, $\mathfrak{ a}$ an ideal of $R$ and $M$ a fixed $R$-module. We introduce and study generalisations of $\mathfrak{a}$-reduced modules, $\mathfrak{R}_{\mathfrak{ a}}$ and $\mathfrak{a}$-coreduced modules,…

The theory of matrix models is reviewed from the point of view of its relation to integrable hierarchies. Discrete 1-matrix, 2-matrix, ``conformal'' (multicomponent) and Kontsevich models are considered in some detail, together with the…

In 1987, C. Sabbah proved the existence of Bernstein-Sato polynomials associated with several analytic functions. The purpose of this article is to give a more elementary and constructive proof of the result of C. Sabbah based on the notion…

The notion of cosilting module was recently introduced as a generalization of the notion of cotilting module. In this paper, we give a characterization of (partial) cosilting modules in terms of two-term cosilting complexes. Moreover, we…

We define sets of orthogonal polynomials satisfying the additional constraint of a vanishing average. These are of interest, for example, for the study of the Hohenberg-Kohn functional for electronic or nucleonic densities and for the study…