nLab moduli stack of curves -- table

Substructure of the moduli stack of curves and the (equivariant) cohomology theory associated with it via the Goerss-Hopkins-Miller-Lurie theorem:

covering					by of level-n structures (modular curve)
	$\ast = Spec(\mathbb{Z})$	$\to$	$Spec(\mathbb{Z}[ [q] ])$	$\to$	$\mathcal{M}_{\overline{ell}}[n]$
structure group of covering	$\downarrow^{\mathbb{Z}/2\mathbb{Z}}$		$\downarrow^{\mathbb{Z}/2\mathbb{Z}}$		$\downarrow^{SL_2(\mathbb{Z}/n\mathbb{Z})}$ (modular group)
moduli stack	$\mathcal{M}_{1dTori}$	$\hookrightarrow$	$\mathcal{M}_{Tate}$	$\hookrightarrow$	$\mathcal{M}_{\overline{ell}}$ (M_ell)	$\hookrightarrow$	$\mathcal{M}_{cub}$	$\to$	$\mathcal{M}_{fg}$ (M_fg)
of	1d tori		Tate curves		elliptic curves		cubic curves		1d commutative formal groups
value $\mathcal{O}^{top}_{\Sigma}$ of structure sheaf over curve $\Sigma$	KU		$KU[ [q] ]$		elliptic spectrum				complex oriented cohomology theory
spectrum $\Gamma(-, \mathcal{O}^{top})$ of global sections of structure sheaf	(KO $\hookrightarrow$ KU) = KR-theory		Tate K-theory ($KO[ [q] ] \hookrightarrow KU[ [q] ]$)		(Tmf $\to$ Tmf(n)) (modular equivariant elliptic cohomology)		tmf		$\mathbb{S}$