All Questions
Tagged with constructible-sheaves sheaf-theory
8 questions with no upvoted or accepted answers
10
votes
0
answers
958
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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
8
votes
0
answers
355
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Why do Kashiwara and Schapira require a base ring of finite global dimension?
In the book "Sheaves on Manifolds" by Kashiwara and Schapira, they work always with sheaves of $R$-modules, where $R$ is a ring of finite global dimension.
Why do they do this, what care ...
- 8,723
5
votes
0
answers
250
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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
5
votes
0
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189
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Constructible sheaves on general stratified spaces
I am not an expert in the field, so my question might be rather standard. Let $X$ be a compact metric space. Assume that $X=\cup_{i=1}^NS_i$ is a finite disjoint union of locally closed topological ...
- 21.8k
2
votes
0
answers
148
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Push-forward of a locally constant sheaf using two homotopic maps
Let $X,Y$ be compact smooth manifolds. Let $f,g\colon X\to Y$ be smooth submersions
(in particular, locally trivial bundles) which are homotopic to each other (in the class of smooth maps, not ...
- 21.8k
2
votes
0
answers
167
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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
2
votes
0
answers
35
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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
1
vote
0
answers
174
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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