Questions tagged [constructible-sheaves]
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65
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Monodromic but not equivariant sheaves and Braden's theorem
Let $X$ be a complex variety with contracting $\mathbb{G}_m$ action. Let $i\colon \{x_0\}\to X$ be the inclusion of the fixed point. Then the simplest case of Braden's theorem (which would then seem ...
- 383
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Fourier transform for perverse sheaves
I am interested in studying the Fourier transform for perverse sheaves on "nice" spaces, say affine complex space stratified by the action of an algebraic group into finitely many orbits.
In ...
- 71
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Lift of nearby cycles functor
Let $S$ be the spectrum of a Henselian discrete valuation ring (called a Henselian trait). Let $f:X\to S$ be a finite type, separated morphism of schemes. Let $\eta\in S$ be the generic point. Let $s\...
- 545
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Find stratification to decompose constructible sheaf to constant parts (example from Wikipedia)
I have a question about techniques used in determining the stratification over which a constructible sheaf falls into even constant pieces demonstrated on this example from Wikipedia.
Let $f:X = \text{...
- 5,780
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154
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Isomorphic IC sheaves induced from different locally closed subvarieties
Let us work with varieties over $\mathbb{C}$ and $D^{b}_{c}(X)$ the bounded constructible derived category of sheaves of $\mathbb{Q}$ vector spaces. Say $X$ and $Y$ are smooth locally closed ...
- 53
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217
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"Simple Limit Argument" in Freitag's and Kiehl's Etale Cohomology
I have a question about an argument used in Freitag's and Kiehl's Etale Cohomology and the Weil Conjecture in the proof of:
4.4 Lemma. (p 41) Every sheaf $F$ representable by an étale scheme $U \to X$,...
- 5,780
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53
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Cohomology of an intermediate extension (perverse) sheaf on the affine line
Let $\mathbb{A}^1$ be defined over a finite field or $\mathbb{C}$, $j: \mathbb{G}_m \rightarrow \mathbb{A}^1$ and $\mathcal{F}$ a local system on $\mathbb{G}_m$. I wonder what is known about the ...
- 195
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139
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Reference request: algebraic characteristic 0 version of microlocalization
I am trying to learn about microlocalization and singular supports with the end goal of understanding at least some form of the coherent-constructible correspondence. I am currently powering through ...
- 1,061
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172
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$\text{Ext}$-groups of perverse sheaves with a fixed stratification
Let $X$ be a complex variety with a good stratification $S$ and consider the category $Perv_S(X)$ of sheaves perverse with respect to the given stratification (with middle perversity) lying in $D^b_S(...
- 1,061
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138
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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 ...
- 21.3k
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412
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Exit path categories of regular CW complexes
Given a finite, regular CW complex $X$ (by regular, I mean that the gluing maps $D^n \to X$ from the closed unit ball to $X$ are homeomorphisms onto their image), denote by $S$ the finite partially ...
- 894
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126
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Local systems as a Serre subcategory of the category of perverse sheaves
Let $X$ be an algebraic variety. Let $Perv(X)$ be the (abelian) category of perverse sheaves on $X$ and let $Loc^{ft}(X)$ be the subcategory of local systems with finitely-generated stalks.
It is ...
- 373
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167
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Fourier transform for constructible sheaves on spheres
Let $S_1 = S_2 = S^d$ be two copies of the $d$-dimensional sphere. Let $p_i : S_1 \times S_2 \to S_i$ be the projection, $j : U \to S_1 \times S_2$ the inclusion of the complement of the diagonal and $...
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196
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Stratified sites/topoi and constructible sheaves
Is it possible to define (possibly derived) categories of constructible sheaves over sites more general than those of open subsets of topological spaces while still retaining essential features, like ...
- 1,472
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435
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Conservativity of stalks of ind-constructible sheaves
I have a simple question about the conservativity of stalks of ind-constructible sheaves. Let $X$ be a topologically noetherian scheme, $S$ a set of geometric points of $X$ corresponding bijectively ...
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