Jacobian varieties of Shimura curves are very interesting objects. For one thing they provide a geometric relation between elliptic curves and modular forms of weight 2 (say we are over $\mathbb{Q}$). So I was wondering what happens when one consider other Shimura varieties, and to start I would be happy to understand the case of $\mathcal{A}\_2$.


Are there references that discuss what kind of abelian variety is the albanese of the Siegel moduli space?


Thank you in advance!



Albanese of Siegel modular variety $\mathcal{A}_2$
Take a look at Sankaran, *Fundamental group of locally symmetric varieties,* Manuscripta (1995), and references therein. I think that the toroidal compactification of $\mathcal{A}\_2$ and related spaces have finite fundamental group, and therefore trivial Albanese.


