Let $f : X \to Y$ be a finite morphism between integral projective schemes of the same dimension over some field, and $\mathcal{F} \in \mathbf{Coh}(X)$. Is it true that $H^n(\mathcal{F})=H^n(f_*\mathcal{F})$?
2026-03-26 17:33:36.1774546416
Is it true for finite morphism $f$ between integral projective schemes that $H^n(\mathcal{F})=H^n(f_* \mathcal{F})$?
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Yes that's true: More generally, the property holds for affine morphisms, see e.g. here