  We construct a canonical compactification $SQ^{toric}_{g,K}$ of the moduli of
abelian varieties over $Z[\zeta_N, 1/N]$ where $\zeta_N$ is a primitive $N$-th
root of unity. This is very similar to, but slightly diferent from the
compactification constructed by the author in Inventiones vol. 136 (1999). Any
degenerate abelian scheme on the boundary of $SQ^{toric}_{g,K}$ is reduced and
singular and it is one of the stable quasi-abelian varieties introduced by
Alexeev and the author (Tohoku J. 1999).
