universal property of Albanese variety

Question

Where can I find proof for the universal property of Albanese variety?

(The universal property of the Albanese variety): For any (smooth projective) variety $X$ over a field $k$, there exists an abelian variety $Alb(X)$ and a morphism $\alpha: X → Alb(X)$ with the following universal property: for any abelian variety $T$ and any morphism $f : X → T$, there exists a unique morphism (up to translation) $ \tilde{f}: A → T$ such that $\tilde{f} \circ α = f$.

Answer 1

This is the definition of the Albanese variety. Presumably you mean something like why the dual of $\mathrm{Pic}^0$ is the Albanese variety in good situations? I've always liked the appendix to this paper of Mochizuki's. In particular, take a look at Proposition A.6.

Answer 2

For a proof see: A. Beauvile Complex Algebraic Surface, Theorem V.13, page 61.