= Grauert base change theorem
{c}
{title2=$(R^qf_*\mathcal F)\otimes k(s)\cong H^q(X_s,\mathcal F_s)$}
For a proper holomorphic map and a coherent sheaf flat over the base, local constancy of the fibre-cohomology dimension makes its higher direct image locally free and gives the displayed base-change identification. Applied to relative holomorphic forms in a smooth proper Kähler family, this constructs the holomorphic <cohomology> bundles entering its <variation of Hodge structure>.
Back to article page
