Coherent cohomology
= Coherent cohomology
{title2=$H^q(X,\mathcal F)$}
= Coherent sheaf cohomology
{synonym}
Coherent cohomology means <sheaf cohomology> with coefficients in a <coherent sheaf>. On a separated <Noetherian scheme>, a finite affine cover computes it using the <Čech cochain complex>, because intersections of affine opens are affine and positive-degree <quasi-coherent sheaf> cohomology vanishes there. Short exact sequences give <long exact sequences in sheaf cohomology>.