Hopkins's equivariant presentation conjecture for the Morava EE-theory homotopy groups

Let KSnK\subset \mathbb{S}_n be a finite subgroup. Let ρEn\rho\in E_n be placed in degree 2-2, let S(ρ)S(\rho) denote the graded symmetric algebra, let NN be a trivial representation corresponding to the multiplicative norm over the group on ρ\rho, and let II be an ideal in degree 00. Hopkins's conjecture. There is a KK-equivariant isomorphism

(En)SW(Fpn)(ρ)[N1]I.(E_n)_*\simeq S_{\mathbb{W}(\mathbb{F}_{p^n})}(\rho)[N^{-1}]^\wedge_I.

This conjectural presentation is intended to make the action of finite subgroups on (En)(E_n)_* easier to describe and compute, supporting calculations involving the homotopy fixed-point and Tate spectra of higher real KK-theories. The source presents it as Hopkins's conjecture, and no resolution is given here.

Sources & referencesView supporting material

Primary source

Drew Heard, “The Tate spectrum of the higher real K-theories at height n=p-1”, arXiv:1501.07759 (2015).

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