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In various descriptions of the moduli space of elliptic curves with level structures, such as the description of $X_0(N)$ being defined over $\operatorname{Spec}\mathbb{Z}[1/N]$, the primitive $N$-th roots of unity pop up.

Is somewhere a description available as to how this connection arises? I mean, somewhere manageable, without wading through the heavy volumes of Deligne & Rapoport or Katz & Mazur?

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