Citation/Abstract

Let E denote the Hopkins-Miller spectrum with [Special characters omitted.] [[ u ₁ ]][ u ^± ] and [Special characters omitted.] the group of automorphisms of a height two formal group Γ over [Special characters omitted.] . The formal scheme Spf ( E _* ) represents *-isomorphism classes of lifts of Γ to [Special characters omitted.] . The group [Special characters omitted.] acts on E _* . Let Γ be the formal group of the completion of the supersingular elliptic curve x ³ + y ³ + z ³ = 0 over [Special characters omitted.] . The universal deformation of this formal group is the completion of x ³ + y ³ + z ³ = 3μ xyz . We calculate the action of the finite group G of elliptic curve automorphisms of x ³ + y ³ + z ³ = 0 and the 3-isogeny [Special characters omitted.] . We form the homotopy fixed-point spectrum E ^hG . We calculate the initial term of the spectral sequence [Special characters omitted.] (0). We show that the initial term of [Special characters omitted.] is the completion of a direct sum of [Special characters omitted.] for various H ⊂ G . We construct a map E ^hG [arrow right] E ^hH , where [Special characters omitted.] , which conjecturally fits into a resolution of [Special characters omitted.] .