Semicontinuity theorem for coherent cohomology
= Semicontinuity theorem for coherent cohomology
For a proper morphism of Noetherian schemes and a coherent sheaf flat over the base, the fiber dimension $s\mapsto\dim_{\kappa(s)}H^p(X_s,\mathcal F_s)$ is upper semicontinuous, and the fiberwise Euler characteristic is locally constant.