All Questions
9 questions
5
votes
3
answers
680
views
Deequivariantisation of indecomposable sheaves
Let G be a connected group acting on a space X. All spaces should be reasonable, so e.g. G is a complex affine algebraic group acting on an algebraic variety X, with everything done using the usual ...
- 8,866
2
votes
0
answers
167
views
Explicit construction of a presentation of a constructible sheaf of $\mathbb{Z}$-modules
This question was prompted by the two following:
Constructible étale sheaves on X are étale algebraic spaces over X
Naive question about constructing constructible sheaves
If I have a ...
- 617
5
votes
0
answers
250
views
Formality of a category of constructible sheaves
Let $X= S^1 \wedge S^1$ be a wedge of circles. Then $X$ admits a natural stratification $\mathcal{S}$ as a union of two disjoint open intervals $I_1, I_2$ and a point $\{*\}$.
Let $D_{\mathcal{S}}(X)$ ...
- 373
10
votes
0
answers
958
views
intuition about perverse sheaves
firstly, I would know if my very basic intuition on perverse sheaves is correct .
secondly, I would have some clarification in what perverse sheaves behaves better than regular sheaves .
my intuition ...
- 546
1
vote
0
answers
174
views
Galoisian perspective on local system tamely ramified along a smooth divisor
This question is about (1.7.8) and (1.7.11) in Deligne’s Weil II paper.
Let $X$ be a regular scheme and $D\subset X$ a smooth principal divisor cut out by the function $t$. Let $\mathcal F$ be a ...
- 1,217
2
votes
0
answers
35
views
If the set of non-0 stalks of F is relatively open, is the same true of its Verdier dual?
Let $X$ be a complex manifold, $F$ a bounded complex of $\Bbb C_X$-modules with constructible cohomology. If the set $\{x: F_x\neq0\}$ is relatively open (i.e. open in its closure), is the same true ...
- 3,079
7
votes
2
answers
839
views
What is the need for torsion in the definition of lisse sheaves?
I am studying the basics of constructible and lisse sheaves, and am trying to understand SGA 4, IX. As Grothendieck himself observes at the beginning of the chapter, one is forced to work with torsion ...
- 5,670
3
votes
1
answer
203
views
Sheaves with $\mathbb{R}$-constructible proper direct image closed under dualizing?
I learned about $\mathbb{R}$-constructible sheaves very recently, so I hope this isn't a silly question:
Let $M$ be a real analytic manifold, and $U\subset M$ an open subanalytic subspace. Denote the ...
- 163
4
votes
1
answer
511
views
Nearby cycles and specialisation - properties
I am looking for reference for properties of nearby cycles - specifically, commutation with non-characteristic pull-back (good enough - commutation with pull-back to closed subvariety which is ...
- 5,562