Chromatic Shifts in the Stable Homotopy Groups of Spheres via Equivariant Elliptic Cohomology

We construct a novel spectral sequence converging to the G-equivariant stable homotopy groups of spheres, G(S), localized at a prime p and height n=2, utilizing the geometry of derived equivariant elliptic cohomology. By analyzing the descent spectral sequence associated with the moduli stack of G-equivariant elliptic curves, we identify a phenomenon of ``chromatic shifting,'' wherein transchromatic periodicities in the fixed-point spectra G(S) manifest as torsion shifts in the equivariant filtration. We prove that for finite abelian groups G, the equivariant elliptic genus induces a faithful detection of -family elements in the Adams-Novikov E2-term, shifted by a factor determined by the dimension of the singular locus of the G-action on the formal group law. This provides a geometric mechanism for the redshift conjecture in the equivariant setting and yields new upper bounds for the order of torsion in kG(S) for k 0.