I have been told about a theorem (it was called Hodge Theorem), which states the following isomorphism:
$H^q(X, E) \simeq Ker(\Delta^q).$
Where $X$ is a Kähler Manifold, $E$ an Hermitian vector bundle on it and $\Delta^q$ is the Laplacian acting on the space of $(0,q)$-forms $A^{0,q}(X, E)$.
Unfortunately I couldn´t find it in the web. Anyone knows a reliable reference for such a theorem? (In specific I´m looking for a complete list of hypothesis needed and for a proof.)
Thank you!