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We prove that the Serre spectral sequence of the fibration$\overline{\mathcal M}_{0, 1+p} \to E\mathbb Z/p \times_{\mathbb Z/p}\overline{\mathcal M}_{0, 1+p} \to B \mathbb Z/p$ collapses at the $E_2$ page.We use this to prove that: for any element of the $\mathbb Z/p$-equivariantcohomology with $\mathbb F_p$-coefficients of genus zero Deligne-Mumford spacewith $1+p$ marked points, if this element is torsion then it isnon-equivariant. This concludes that the only "interesting" $\mathbbZ/p$-equivariant operations are quantum Steenrod power operations.

The $\mathbb Z/p$-equivariant cohomology of genus zero Deligne-Mumford space with $1+p$ marked points