Let $g,n$ be positive integers, is there a reference that $\mathrm{Sp}(2g,\mathbb{Z})\to\mathrm{Sp}(2g,\mathbb{Z}/n\mathbb{Z})$ is surjection?


The only reference I could find is lemma 5.16 in Deligne–Mumford, but to be honest, I don't quite understand the argument: Why is the reduction map surjective on unipotent elements?


[Deligne and Mumford - The irreducibility of the space of curves of given genus](http://www.numdam.org/article/PMIHES_1969__36__75_0)



Reduction mod $n$ of symplectic group
This was originally proved in


M. Newman, J. R. Smart, [Symplectic modulary groups](https://eudml.org/doc/207465), Acta Arith 9 (1964), 83-89.


