Related papers: A Localization Algorithm for $D$-modules

Let $d$ be a positive integer and $\mathbb H$ be an integrally closed subring of a global function field $F$. The purpose of this paper is to provide a general sieve method to compute densities of subsets of $\mathbb H^d$ defined by local…

In this paper we prove the constructibility on the subanalytic sites of the sheaves of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. Such a result solves a conjecture of M. Kashiwara and P. Schapira…

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…

On a complex symplectic manifold we prove a finiteness result for the global sections of solutions of holonomic DQ-modules in two cases: (a) by assuming that there exists a Poisson compactification (b) in the algebraic case. This extends…

Let $F$ be a field, let $D$ be a subring of $F$, and let ${\mathfrak{X}}$ be the Zariski-Riemann space of valuation rings containing $D$ and having quotient field $F$. We consider the Zariski, inverse and patch topologies on…

We study the moduli and determine a homotopy type of the space of all generalized Morse functions on d-manifolds for given d. This moduli space is closely connected to the moduli space of all Morse functions studied in the paper…

Let $R=\mathbb{F}_p[x_1,\ldots,x_n]$ and let $\mathbf{F}$ be the ring of Frobenius operators over $R$. We introduce a notion of Bernstein dimension and multiplicity for the class of finitely generated $\mathbf{F}$-modules whose structure…

We introduce a concept of a fractional-derivatives series and prove that any linear partial differential equation in two independent variables has a fractional-derivatives series solution with coefficients from a differentially closed field…

We investigate the notions of \emph{localization} and \emph{filtration} in the context of extended affine Lie algebras. Our primary objective is to develop a localization theory that facilitates the construction of meaningful local…

In this paper, we consider modular local polynomials. These functions satisfy modularity while they are locally defined as polynomials outside of an exceptional set. We prove an inequality for the dimension of the space of such forms when…

We compute the anomalies of the topological A and B models with target space geometry of Hitchin's generalized type. The dimension of the moduli space of generalized holomorphic maps is also computed, which turns out to be equal to the…

We present a new algorithm for solving the reduction problem in the context of holonomic integrals, which in turn provides an approach to integration with parameters. Our method extends the Griffiths--Dwork reduction technique to holonomic…

Volume of moduli space of BPS vortices on a compact genus h Riemann surface Sigma_h is evaluated by means of topological field theory and localization technique. Vortex in Abelian gauge theory with a single charged scalar field (ANO vortex)…

Tauchi provides an example illustrating the action of a real algebraic subgroup $H$ of $GL(2n, \mathbb{R})$ with finitely many orbits on $\mathbb{R}^{2n}$, while the dimension of the space of relative $H$-invariant distributions on…

We study universal localisations, in the sense of Cohn and Schofield, for finite dimensional algebras and classify them by certain subcategories of our initial module category. A complete classification is presented in the hereditary case…

In this article, we develop a positive characteristic analogue of the Bernstein--Sato theory for holonomic D-modules in the complex setting. We work with D-modules on a Noetherian regular $F$-finite $\mathbb{F}_p$-scheme $X$, and define…

Based on the recent progress in the irregular Riemann-Hilbert correspondence for holonomic D-modules, we show that the characteristic cycles of some standard irregular holonomic D-modules can be expressed as in the classical theorem of…

We study quotients of the Weyl algebra by left ideals whose generators consist of an arbitrary Z^d-graded binomial ideal I along with Euler operators defined by the grading and a parameter in C^d. We determine the parameters for which these…

We study the moduli space of $d$-dimensional linear subspaces contained in a fixed $(d+1)$-dimensional linear variety $X$, and its tropicalization. We prove that these moduli spaces are linear subspaces themselves, and thus their…

We describe all possible universal localisations of a hereditary ring in terms of suitable full subcategories of the category of finitely presented modules. For these universal localisations we then identify the category of finitely…