# Reference request for “Hodge Theorem”

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!

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