Questions tagged [perverse-sheaves]
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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 ...
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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 ...
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What advantages do perverse sheaves provide over D-modules? (or vice versa)
My question is as in the title: What advantages do perverse sheaves provide over D-modules? (or vice versa)
As a specific example: could something like the modular generalized Springer correspondence ...
- 355
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Decomposition theorem for resolution of surface singularity
I’ve asked this question on MSE but I don’t get an answer, so I’m trying to ask here.
https://math.stackexchange.com/questions/4914142/decomposition-theorem-for-resolution-of-surface-singularities
In ...
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Is inverse image along finite group quotient $t$-exact for the perverse $t$-structure?
Let $q: \mathbb{C}\to \mathbb{C}$ be the quotient by $\mathbb{Z}/n\mathbb{Z},$ i.e. the map taking $z\mapsto z^n$. In the accepter answer to Operations on perverse sheaves on disk the inverse image of ...
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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 ...
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Are there any relations between perverse t-structure (cohomologies) and standard t-structure (cohomologies)?
I'm reading the Corollary 3.2.3. in Exponential motives by J. Fresan and P. Jossen.
The authors use the following statement in the proof of Corollary 3.2.3: let $C$ be any object in the derived ...
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$\pm 1$-equivariant perverse sheaves on the affine line
Let $G=\mathbb{Z}/\mathbb{2Z}$ act by the map $z\mapsto -z$ on a complex line $\mathbb{C}$. The category $\mathcal{Perv}(\mathbb{C})$ of perverse sheaves smooth along the stratification by the origin ...
- 1,061
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Are perverse sheaves representations of some topological invariant?
The well-known correspondence between vector bundles with flat connection on a smooth complex algebraic variety $X$ and complex representations of $\pi_1(X^{an})$, the fundamental group of the ...
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Do the nearby cycle and Beilinson's vanishing cycle functors commute?
Let $X$ be a complex algebraic variety with a pair of regular functions $f_1,f_2$. To these functions we can associate various functors: the nearby cycles functor $\Psi_{f_i}$, the vanishing cycles ...
- 1,061
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Intersection cohomology and Poincaré duality
When trying to learn about perverse sheaves I hand-wavingly thought that intersection cohomology is the ‘minimal’ way of fixing the failure of Poincaré duality. But I am very aware that it is risky to ...
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How to think about Beilinson's gluing data?
Let $X$ be a complex manifold, $D$ a divisor (that is globally the zero locus of a function) and $U$ its complement. Recall Beilinson's "how to glue perverse sheaves":
Given a perverse ...
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Simpson correspondence for perverse sheaves
Let $X$ be a projective complex manifold. Then Simpson's correspondence from nonabelian Hodge theory shows that the category of semisimple local systems on $X$ is equivalent to the category of ...
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Applications of the Riemann-Hilbert Correspondence
I am aware of the (first) proof of the Kazhdan–Lusztig conjectures using the Riemann-Hilbert Correspondence. Are there any other interesting applications of the RH correspondence?
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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 ...
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