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Results tagged with perverse-sheaves
Search options questions only
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user 2837
1
vote
1
answer
1k
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Intermediate extension functor exact?
It is well known, that the intermediate extension functor $j_{!*}$ preserves injections and surjections. However it seems that it is not exact in general!
1) What would be an example which shows that …
- 13.2k
7
votes
1
answer
435
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Perverse sheaves for easy stratifications
Let $X$ be a complex variety equipped with a stratification. Let us assume, that all strata are contractible and in addition, that all strata closures are smooth.
Is there an "easy" quiver descriptio …
- 13.2k
5
votes
3
answers
917
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Reference for two facts about perverse sheaves on G/B
I wonder whether there is a reference for the following two things:
The Grothendieck group of B-equivariant semisimple? perverse sheaves on $G/B$ is the Hecke-algebra.
The category of B-equivariant …
- 13.2k
0
votes
0
answers
251
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Online reference for bridge between $\mathbb C$ and $\mathbb F$
I am looking for a text which
1) Explains how to deduce statements about perverse sheaves on complex geometry from analogous statements in positive characteristic. For example the last chapter "De F …
- 13.2k
3
votes
1
answer
413
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How to glue perverse sheaves of abelian groups?
Let $X$ be a complex algebraic variety and consider the category $P(X)$ of perverse sheaves of complex vector spaces.
Let $f:X\rightarrow \mathbb C$ be a regular function, $Z$ its zero set and $U$ it …
- 13.2k
6
votes
1
answer
497
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Geometric interpretation of translation through the wall
What does translation through the wall correspond to under Beilinson Bernstein localization?
More precisely I am interested in the following:
There is a well known equivalence between the principal …
- 13.2k
14
votes
2
answers
1k
views
Relation between holonomic D-modules and perverse sheaves
Given a smooth complex algebraic variety, the Riemann-Hilbert-correspondence tells us, that the category of perverse sheaves is equivalent to the category of regular, holonomic D-modules.
However not …
- 13.2k
5
votes
1
answer
753
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Easy special cases of the decomposition theorem?
The decomposition theorem states roughly, that the pushforward of an IC complex,
along a proper map decomposes into a direct sum of shifted IC complexes.
Are there special cases for the decomposition …
- 13.2k
4
votes
0
answers
539
views
Geometric picture behind tilting sheaves
I am trying to read "Tilting exercises" and have trouble to see any geometric pictures behind the formulas.
So my questions are, how to think about tilting perverse sheaves?
Are they just formal ga …
- 13.2k
7
votes
3
answers
714
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Nice algebraic approximations of classifying spaces
Let $G=GL_k(\mathbb C)$ be the complex linear group. Then the infinite Grassmannian is a model for the classifying space $BG$.
We can write the infinte Grassmannian as a colimit of the finite Grassma …
- 13.2k
19
votes
0
answers
414
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Constructible derived category and fundamental category
Introduction (may be skipped)
Given a nice topological space $X$, the category of local systems (say over a field $k$) on it is equivalent to the category of representations of its fundamental groupo …
- 13.2k