All Questions
Tagged with derived-categories perverse-sheaves
9 questions with no upvoted or accepted answers
8
votes
0
answers
350
views
Beilinson's theorem for fixed stratifications
Beilinson's theorem states that for a variety $X$ and a field $k$ the realization functor
$$\text{real}: D^b\text{Perv}(X,k)\to D_c^b(X,k)$$ is an equivalence of categories.
If we only consider ...
- 1,071
8
votes
0
answers
751
views
What's the definition of a microlocal sheaf?
I'm slowly becoming familiar with what microsupport of a sheaf is, but none of the references I've seen give a definition of what a microlocal sheaf should be in general.
In this paper of ...
- 191
4
votes
0
answers
291
views
The associated graded of a mixed Hodge module
Unfortunately this question will be a bit vague, since the question revolves around a memory of something I may have heard in a talk (long time ago).
Let $X$ be a smooth complex variety. Let $MHM(X)$ ...
- 1,595
3
votes
0
answers
424
views
Stalks of perverse cohomology sheaves?
For a complex of sheaves $\cal{F}^{\bullet}$ on a variety $X$, a useful fact is that the stalks of the cohomology sheaves of $\mathcal{F}^{\bullet}$ agree with the cohomology groups of the complex of ...
- 1,701
2
votes
0
answers
174
views
Perverse sheaves and maximal genus Gopakumar-Vafa invariants
Let $f: X \to Y$ be a proper morphism between complex varieties (the varieties as well as the map may be non-smooth) and let $\phi \in \text{Perv}(X)$ be a perverse sheaf on $X$. Given this data, it ...
- 1,701
2
votes
0
answers
103
views
Does intermediate extension functor commutes with forgetful functor in equivariant derived category?
The forgetful functor from $D^b_G(X)$ to $D^b(X)$ carries $Perv_G(X)$ to $Perv(X)$ by definition $5.1$ in the book of Bernstein and Lunts. My question is do the following functors, intermediate ...
- 677
1
vote
0
answers
170
views
Espace étalé for derived category
It is known that for a sheaf $\mathcal{F}$ on $X$, we can associate $X_\mathcal{F}$, the étalé space of $\mathcal{F}$ over $X$ such that section of $X_\mathcal{F}$ coincides with section of $\mathcal{...
- 677
0
votes
0
answers
346
views
on the Springer sheaf
Let $\pi:\tilde{\mathfrak{g}}\rightarrow \mathfrak{g}$, be the Grothendieck-Springer resolution, where $\mathfrak{g}$ is a semisimple Lie algebra over $\mathbb{C}$.
We know that $\pi$ is small thus $\...
- 3,472
0
votes
0
answers
150
views
descent of a complex of sheaves
Let X a projective variety over an algebraically closed field on which an abelian variety $A$ acts freely.
Then $X/A$ is a projective variety. Let $f:X\rightarrow X/A$
Let $K\in D_{c}^{\leq 0}(X,\bar{...
- 3,472