For $E$ an elliptic curve, let $LS(E)$ be the group of line bundles on $E$ with a flat connection. This is an $\mathbb{A}^1$-torsor over $E^\vee$. By Riemann-Hilbert (since the gau …

Hello, Suppose that $k$ is an algebraically closed field of char. 0. Let $X$ be a smooth connected variety over $k$. Then I have the category $A$ of Regular Singular smooth $D$- …

I am just a beginner in $D$-module, so this could be a stupid question, but I can't find an easy reference for it. I would like to define the notion of $D$-affine morphism. The mos …

If we have filtration on D-module compatible with some good filtration on differential operators sheaf then adjoint graded module is module over functions on cotangent bundle. So m …

For a smooth complex variety, one can consider the category of say holonomic $\mathcal D$ modules on it. It is equipped with the deRham functor, which turns a $\cal D$-module into …

Suppose that $X$ is an algebraic variety over $\mathbb C$, not necessarily smooth. Is it still true that each $\mathcal D_X$-module ($\mathcal D_X$ is of course the sheaf of differ …

Let $V$ be a finite dimensional vector space over $\mathbb{C}$, denote $V^{\times} = V -0$ and let $\pi : V^{\times} \rightarrow \mathbb{P}(V)$ be the quotient by the natural actio …

In Chriss and Ginzburg's book "Representation Theory and Complex Geometry" as well as the paper "Geometric Methods in Representation Theory of Hecke Algebras and Quantum Groups", t …

The Riemann-Hilbert correspondence, as proved by Kashiwara and Mebkhout, says that for X a smooth algebraic variety over $\mathbb{C}$ there is an equivalence of triangulated catego …

Hello, I omit in the following all the words "derived, twisted, holonomic, finitely-generated...". We have the Bernstein-Beilinson equivalence between the category of $N$-equivar …

Suppose $f:X\to Y$ is a map of smooth complex algebraic varieties. There is a pushforward functor $f_\ast : D(X) \to D(Y)$ on the derived category of $D$-modules. This certainly …

I am trying to come to grips with Saito's theory of mixed Hodge modules (slightly) beyond just the basic axiomatic formalism. I will take my Hodge structures and sheaves to be rati …

My question is regarding the definition of $\mathcal{D}$-modules of level $m$ given in this paper. As an example, let $X=\mathbb{A}^1$ over $S=\text{Spec }\overline{\mathbb{F}_p}$; …

This question is related to my other question. Consider a scheme $X$ over $S=\text{Spec}(\mathbb{k})$ where $\mathbb{k}=\overline{\mathbb{F}_p})$; let $F: X \rightarrow X$ be the F …

Let $X$ be a smooth $\mathbf{C}$-scheme of finite type. In section 7.2 of their preprint "Quantization of Hitchin's Integrable System and Hecke Eigensheaves", Beilinson and Drinfel …