4
votes
0answers
300 views
Localization of vanishing cycles
Consider a regular holonomic D-module (or a perverse sheaf) $M$ on a smooth variety $X$. Let $f:X\to A^1$ be a polynomial (or holomorphic) function.
Question: Is it true that the …
8
votes
1answer
202 views
The Infinitesimal topos in positive characteristic
This question was inspired by and is somewhat related to this question.
In his article "Crystals and the de Rham cohomology of schemes" in the collection "Dix exposes sur la cohom …
7
votes
1answer
221 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 …
18
votes
1answer
471 views
D-modules, deRham spaces and microlocalization
Given a variety (or scheme, or stack, or presheaf on the category of rings), some geometers, myself included, like to study D-modules. The usual definition of a D-module is as she …
4
votes
0answers
88 views
V-filtration of D-modules associated to a monomial
Hi
In Mixed Hodge modules Saito computes the Verdier specialisation of a D-modules with respect to a monomial $g = x_1^{m_1}\ldots x_n^{m_n}$. This is a very nice result as I find …
11
votes
3answers
405 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 cons …
12
votes
3answers
377 views
How do I compare the different notions of Fourier transform for sheaves?
There is a close but not perfect relationship between algebraic D-modules on C^n, constructible sheaves on C^n in the analytic topology, and \ell-adic sheaves on an n-dimensional v …
6
votes
3answers
245 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 algebra …
1
vote
0answers
97 views
Sebastiani-Thom isomorphism for D-modules
Considering $f:X\to \mathbb{C}$, $g:X\to \mathbb{C}$ and $f\oplus g:(x,y)\mapsto f(x)+g(y)$.
The Sebastiani-Thom isomorphism is an isomorphism $\Phi_{f\oplus g}(M\boxtimes N) = \P …
3
votes
3answers
378 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-mo …
3
votes
1answer
176 views
what is the connection between D-modules and coordinate bundles?
fix n and a field k of characteristic zero. let G be the pro-algebraic group of automorphims of k[[x_1,...x_n]]. let G_0 be the subgroup of automorphisms preserving the closed po …
