de Rham theorem ($H_{\mathrm{dR}}^k(M;\mathbb{C})\cong H^k(M;\mathbb{C})$)

The complex of smooth differential forms resolves the constant complex sheaf by the Poincare lemma and consists of fine sheaves. Its global cohomology therefore agrees with sheaf cohomology of that constant sheaf. A good-cover Čech-de Rham double complex gives an explicit comparison, used in Čech-de Rham curvature descent.