de Rham theorem
= de Rham theorem
{c}
{title2=$H^k_{\mathrm{dR}}(M;\mathbb C)\cong H^k(M;\mathbb C)$}
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>.