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Results tagged with perverse-sheaves
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user 1985
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The conjectural relation between mixed motivic sheaves and the perverse t-structure.
For triangulated category of geometric motives over a regular scheme $S$, the $\ell$-adic realisation has been constructed by Florian Ivorra in his thesis. I think the functor is expected to be t-exac …
- 7,527
10
votes
Accepted
Relation between holonomic D-modules and perverse sheaves
The answer is yes but it's not easy. You need additional data to describe the irregular part of your connexion. These are known as Stokes structures. Very loosely it's a filtration of your sheaf of so …
- 7,527
4
votes
Computation of vanishing cycles
Here's the bottom line. If $F$ is a perverse sheaf or a D-module, there is an isomorphism between $\psi_fF$ and the complex $[\psi \psi F \to \psi \phi F \oplus \phi \psi F]$. The reason why we can't …
- 7,527
4
votes
Is there a 'classical' definition for the support of a perverse sheaves.
Let $j_i : U_i \hookrightarrow X$ open immersions and $j: U_1 \cup U_2 \hookrightarrow X$. If $j_1^*F = j_2^*F = 0$ then $j^*F = 0$ by considering a Mayer-Vietoris triangle. So there is a largest open …
- 7,527
6
votes
Localization of vanishing cycles
An answer to this question was given to me by Pierre Schapira. This is known as the microlocal Bertini-Sard theorem (cf. Sheaves on manifolds cor. 8.3.12).
Consider a map $f:X\to A^1$. It induces $f …
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