Proper base change for sheaves
= Proper base change for sheaves
{title2=$(Rf_*E)_y\cong R\Gamma(f^{-1}(y),E)$}
For a proper map of locally compact spaces and a constructible complex $E$, the derived stalk satisfies $(Rf_*E)_y\cong R\Gamma(f^{-1}(y),E|_{f^{-1}(y)})$. In particular $(R^if_*\mathbb Q)_y\cong H^i(f^{-1}(y);\mathbb Q)$. Properness is what prevents fibre <cohomology> from missing nearby sections.