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I am searching for a reference for the generalized Bloch conjecture for surfaces. I know that it states that $CH(S)$ is finitely generated if and only if $H^q(S,\Omega^p)=0$, for $q\neq p$, but where I can find it?

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You can look at the book "Hodge Theory and Complex Algebraic Geometry, Volume 2" by Claire Voisin, Chapter 11. References to the original papers can be found in the bibliography of the book. Here is a link http://books.google.de/books?id=Yqe6eRGTQfcC&printsec=frontcover#v=onepage&q&f=false

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