Related papers: D-modules on rigid analytic spaces

We define global and local Weyl modules for Lie superalgebras of the form $\mathfrak{g} \otimes A$, where $A$ is an associative commutative unital $\mathbb{C}$-algebra and $\mathfrak{g}$ is a basic Lie superalgebra or $\mathfrak{sl}(n,n)$,…

We establish a relation, conjectured recently by E. Witten, between the hypermultiplet moduli space in compactifications of the heterotic string on an A-D-E singularities, and the moduli spaces of three dimensional pure gauge theories with…

We describe the generic modules in each component of the spaces of representations of certain string algebras. In so doing, we calculate the dimensions of higher self-extension groups for generic modules. This algorithm lends itself for use…

We study modules for the divided power algebra $D$ in a single variable over a commutative noetherian ring $k$. Our first result states that $D$ is a coherent ring. In fact, we show that there is a theory of Gr\"obner bases for finitely…

The aim of this note is to introduce the notion of a $\operatorname{D}$-Lie algebra and to prove some elementary properties of $\operatorname{D}$-Lie algebras, the category of $\operatorname{D}$-Lie algebras, the category of modules on a…

We study the classification of D-branes in all compact Lie groups including non-simply-laced ones. We also discuss the global structure of the quantum moduli space of the D-branes. D-branes are classified according to their positions in the…

We will adopt an elementary approach to D-modules on Ran spaces in terms of two-limits; the aim here is to define the category of coherent D-modules, characteristic varieties and non-characteristic maps. An application will be the proof of…

We study the localization functor from the category of representation of Lie super-algebra $\mathfrak{g} = \mathfrak{gl}(m, n)$ into monodromic D-modules on the flag manifold $X = G/B$. We show that the right localization is monadic in a…

We introduce a formalism of Hochschild (co)-homology for $\mathcal{D}$-cap modules on smooth rigid analytic spaces based on the homological tools of Ind-Banach $\mathcal{D}$-cap modules. We introduce several categories of $\mathcal{D}$-cap…

The simple finite Lie superalgebras D(2,1;\alpha), G(3), D(4,1), D(2,2), A(3,1) and F(4) admit D-module representations, given by a set of differential operators of a single real variable t, at a critical value of the scaling dimension…

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 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…

We discuss the concepts of fine and coarse moduli spaces in the context of finite dimensional algebras over algebraically closed fields. In particular, our formulation of a moduli problem and its potential strong or weak solution is adapted…

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 make an initial study on type D moduli spaces in positive characteristic $p\neq 2$, where we allow $p$ ramified in the definite quaternion algebra. We classify the isogeny classes of $p$-divisible groups with additional…

We reinterpret and generalize the construction of local Shimura varieties and their non-minuscule analogs by viewing them as moduli spaces of admissible pairs. Our main application is a bi-analytic Ax-Lindemann theorem comparing, in the…

We translate notions and results of decomposition and dimension theories for module categories, into the lattice environment. In particular we translate dimension theory in module categories to complete modular upper-continuous lattices.

In this paper we prove the preconstructibility of the complex of tempered holomorphic solutions of holonomic D-modules on complex analytic manifolds. This implies the finiteness of such complex on any relatively compact open subanalytic…

Let V be the space of 2x2x2 complex hypermatrices, endowed with the natural group action of GL=GL(2,C)^3. The category of GL-equivariant coherent D-modules on V is equivalent to the category of representations of a quiver with relations. In…

We study the $p$-adic analogue of the $\ell$-adic hypergeometric sheaves for reductive groups, called the hypergeometric $\mathscr{D}^{\dagger}(\infty)$-modules. They are overholonomic objects in the derived category of arithmetic…