%0 Journal Article %T Full level structures revisited: pairs of roots of unity %A Preston Wake %J Mathematics %D 2015 %I arXiv %X We introduce a notion of full level structure for the group scheme $\mu_p \times \mu_p$, and show that scheme of full level structures is flat over $\Bbb{Z}$. %U http://arxiv.org/abs/1506.01750v1