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Nov 13 at 5:25 comment added Will Sawin You have to define the proper smooth pushforward using a version of the algebraic de Rham complex. This is often presented as part of the theory of Riemann-Hilbert correspondence for D-modules.
Nov 13 at 3:47 comment added Satan's Minion This is already false if $Y$ is a point: cohomology of the structure sheaf is not the $\mathbf{C}$-linearization of singular cohomology.
Nov 13 at 2:02 history asked Richard CC BY-SA 4.0