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I am trying to understand "de Cataldo, Migliorini. The perverse filtration and the Lefschetz hyperplane theorem. Annals of Mathematics, 171(2010), 2089-2113." My question is about one detail in the ...

Show that a perverse sheaf on $\mathbb{A}^1(\mathbb{C})$ (the complex plane with the analytic topology) is a bounded complex $A$ of sheaves of $\mathbb{Q}$-vector spaces with constructible cohomology ...

For a complex of sheaves $\cal{F}^{\bullet}$ on a variety $X$, a useful fact is that the stalks of the cohomology sheaves of $\mathcal{F}^{\bullet}$ agree with the cohomology groups of the complex of ...