All Questions
Tagged with perverse-sheaves d-modules
15 questions with no upvoted or accepted answers
9
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446
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$K$-theory of $D$-modules
I have to admit I don't know much about topics appearing in this question, I just see very rough connections between these objects:
According to this page 23, a different $t$-structure on $D^b(\text{...
- 5,901
7
votes
0
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207
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A reference for Bernstein's approach to KL conjectures
The exposition in the famous J. Bernstein's lecture notes on D-modules is rather sketchy.
Fortunately, there are many other sources for the information from this text (like Hotta's excellent "D-...
- 81
6
votes
0
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230
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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
6
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0
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225
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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 ...
- 495
6
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0
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275
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The geometric "hands-on" vs. algebraic approach to nearby cycles
Feel free to skip to the question below; the following is just context and discussion:
An interesting, but seemingly less used result in the theory of nearby cycles of constructible sheaves is (...
- 272
6
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0
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233
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Toric Degenerations and Nearby Cycles
Suppose that $f: X \to \mathbb{A}^1$ is a toric degeneration in the sense of Nishinou-Siebert. In other words let X be a (possibly singular) toric variety equipped with a (not necessarily proper) ...
- 1,543
6
votes
0
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714
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Characteristic Cycles and Nearby Cycles
Let $Y$ be a smooth algebraic variety over $\mathbb{C}$, let $X = Y \times \mathbb{C}$ and let $f: X \to \mathbb{C}$ be the projection. Let $M$ be a (not necessarily regular) holonomic $D_X$-module ...
- 1,543
6
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0
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391
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Blow ups and Characteristic varieties
Let $f:Y\to X$ be a morphism of smooth varieties (complex analytic or algebraic as you wish). We have
$$
T^* Y \overset{f_d}{\longleftarrow} Y\times_X T^*X \overset{f_\pi}{\longrightarrow} T^* X
$$...
- 7,527
4
votes
0
answers
117
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Is there an "$\ell$-adic Riemann Hilbert correspondence"?
The Riemann-Hilbert correspondence (see, e.g., Thm. 7.2.2 of D-modules, perverse sheaves, and representation theory) shows that analytic perverse sheaves are equivalent to regular holonomic $D$-...
- 615
4
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0
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200
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D-modules generated by derivatives of Delta function
We consider D-modules over the affine line $\mathbb{A}_{\mathbb{C}}^{1}$, i.e. modules of Weyl algebra $A_1(\mathbb{C})=\mathbb{C}[x,\partial]$. There is a set of microfunctions (ref. A Primer of ...
- 121
4
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344
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Absolute purity for intersection cohomology
If $i:Z\hookrightarrow X$ is a closed embedding of codimension $c$, then
$$i^*k_X\ =\ k_Z , \ \ \ i^!k_X\ \stackrel{(\star)}{=}\ k_Z[2c]$$
where $(\star)$ is true when $i$ is in addition regular.
Here ...
- 5,701
4
votes
0
answers
290
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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
76
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Is the characteristic cycle map for perverse sheaves injective?
Let $X$ be a smooth irreducible complex variety. Is the characteristic cycle map from the Grothendieck group of perverse sheaves (with complex coefficients) on $X$ to the free abelian group generated ...
- 333
2
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0
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112
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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?
- 507
1
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0
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172
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When does a $D$-module think it’s a pullback along a smooth morphism?
Let $X$ and $Y$ be two algebraic varieties, and let $f: X \to Y$ be a morphism. Suppose $A$ is a holonomic $D$-module on $Y$. In this situation we can pull $A$ back to $X$ using either the $!$ or $*$ ...
- 3,019