1
vote
0answers
209 views

D-modules as quantization of modules on cotangent bundle

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 morally D-module is ...
1
vote
0answers
150 views

Non-characteristic is to pullback as (blank) is to pushforward.

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 does not preserve ...
9
votes
0answers
261 views

Duality in category O vs. Duality of D-modules

Hello, I omit in the following all the words "derived, twisted, holonomic, finitely-generated...". We have the Bernstein-Beilinson equivalence between the category of $N$-equivariant $D$-modules on ...
5
votes
1answer
370 views

l-adic Turrittin

What would be an l-adic analogue of the Turrittin-Levelt decomposition theorem? Turrittin-Levelt is a structure theorem of meromorphic connections on a complex curve in the formal neighbourhood of a ...
2
votes
1answer
441 views

Is base affine space a trivial fibration?

I am very confused about the base affine space. Let $G$ be a complex reductive algebraic group and $H=B/U$ the abstract torus. If I understand it correctly (Edit: which turns out not to be the case! ...
0
votes
0answers
184 views

Does regularity of a D-module for an unusual filtration imply regularity for the usual one?

One definition of regular D-modules on affine space is that a D-module is regular if it has a filtration compatible with the order filtration on differential operators whose associated graded is ...
7
votes
0answers
377 views

Status of Borho and Brylinski's irreducibility conjectures?

In Differential Operators on Homogeneous Spaces, III, Section 6.7, Borho and Brylinski make a long series of equivalent conjectures which they show are all equivalent. Perhaps the easiest statement ...
1
vote
1answer
462 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 ...
7
votes
4answers
1k views

Gluing perverse sheaves?

It might be a stupid question. How to glue perverse sheaves? I am considering the following example. Flag variety of $sl_2$, which is $P^1$. Consider category of perverse sheaves on $P^1$. Denoted ...
10
votes
1answer
1k views

What is the recent development of D-module and representation theory of Kac-Moody algebra?

I just started to collect the papers of this field and know little things. So if I make stupid mistake, please correct me. It seems that there are several approaches to localize Kac-Moody algebra(in ...
6
votes
3answers
701 views

Making D-modules on affine varieties more explicit

This is a follow up to my question about D-modules supported on the nilpotent cone. I got some good answers there but now I have a more basic question. Consider an affine algebraic variety X, a ...
11
votes
3answers
981 views

D-modules supported on the nilpotent cone

I am reading some papers which involve D-modules on a Lie algebra g, which are supported on the nilpotent cone n. They are equivariant for the action of G. (In particular, I consider g=sl_n). It ...
6
votes
3answers
2k views

Beilinson-Bernstein and Koszul duality

For geometric representation theorists down here. Consider the Beilinson-Bernstein theorem: Functor of global sections establishes the correspondence between twisted D-modules with fixed ...