3
votes
1answer
340 views

The Weyl algebra modules which are also rings

Consider the space $C^\infty(\mathbb{R})$. We have on it a natural action of the Weyl algebra generated by $x$ and $d/dx$, where $x$ is the coordinate on $\mathbb{R}$, and there is plenty of Weyl ...
1
vote
1answer
147 views

Most general “finiteness of de Rham cohomology” statement for holonomic $D$-modules in the algebraic case?

Let $X$ be a nonsingular algebraic variety over a field $k$ of characteristic zero. (We may assume $k$ algebraically closed if need be, but I want to avoid specifically demanding $k = \mathbb{C}$.) ...
1
vote
0answers
140 views

Characteristic variety of a D-module along smooth pullback

All varieties are over the complex numbers. Given a smooth variety $X$, write $T^* X$ for its cotangent bundle. For a morphism of smooth varieties $f: X \to Y$ write $f_{\pi}: T^*Y \times_Y X \to ...
6
votes
0answers
211 views

Non-characteristic maps (ala D-modules)

I am trying to understand a `well known' fact (see Kashiwara'sIntroduction to microlocal analysis page 63, remark 4.8) about non-characteristic morphisms. Here is ...
11
votes
1answer
636 views

On the definition of regularity

In the litterature on D-modules, there are many definitions of regularity of holonomic D-modules. (1) Bernstein first defines regularity on a curve then says a holonomic D-module is regular if its ...
5
votes
1answer
452 views

Reconstruction from category of D-modules on variety

Arinkin has a theorem which says that an abelian variety can be reconstructed from its derived category of coherent D-modules. D.Orlov conjectured that this theorem is true for any variety. My ...
1
vote
1answer
556 views

Is simple non-holonomic D-module a local concept?

It is well known that we can use the Riemann-Hilbert correspondence to describe holonomic D-modules in terms of a category of perverse sheaves on some variety $X$. And $U|\rightarrow Perv(U)$ is a ...
1
vote
3answers
238 views

TDO basic facts reference request

Hello, where can I read about some basic properties of twisted D-Modules? I would like to know, a reference, that describes how to glue these modules together/pull them back/push them forward.