The ℤ∕p-equivariant cohomology of thegenus-zero Deligne–Mumford space with 1 + p marked points

We prove that the Serre spectral sequence of the fibration M 0;1Cp !EZ=p Z=p M 0;1Cp !BZ=p collapses at the E 2 -page.We use this to prove that a torsion element of the Z=p-equivariant cohomology with F p -coefficients of genus-zero Deligne-Mumford space with 1 C p marked points is lifted from nonequivariant cohomology.We conclude that the only "interesting" Z=p-equivariant operations on quantum cohomology are quantum Steenrod power operations.