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There is a well known theorem that says that the functor associating to a perverse sheaf $F$ on $X$ the data $(F|_U,\phi_f(F),can:\psi_f(F) \to \phi_f(F),var:\phi_f(F)\to \psi_f(F)(-1))$ where $U = X …

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 $ …

Here's the problem I'm looking at: $F$ is a perverse sheaf (or a regular holonomic D-module, or even a mixed hodge module) on $\mathbb{C}^2$ stratified by $z_1 = 0$, $z_2=0$. It can be caracterized …

Consider a regular holonomic D-module (or a perverse sheaf) $M$ on a smooth variety $X$. Let $f:X\to A^1$ be a polynomial (or holomorphic) function. Question: Is it true that the $\lambda \in A^1$ s …

(1) In "Geometrie Microlocale", Verdier states the following theorem. Theorem: Let $E$ be a vector space and $F$ a constructible complex on $E$. Then for $\ell$ a linear form on $E$, we have a morph …

Ok so there's a lot of litterature about nearby cycles functor since it was introduced by Grothendieck and Deligne but I couldn't find any clear answer to the following natural question: Problem: Let …