Morava E-theory of symmetric groups

Strickland, Neil P.

doi:10.1016/s0040-9383(97)00054-2

Cited by 66 publications

(73 citation statements)

References 18 publications

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“…One starting point for making the connection between algebraic geometry and power operations is Strickland's theorem [Str98] which gives an algebro-geometric interpretation of E 0 (BΣ p k )/I tr .…”

Section: A Theorem Of Ando-hopkins-stricklandmentioning

confidence: 99%

Lubin-Tate theory, character theory, and power operations

Stapleton¹

2020

Handbook of Homotopy Theory

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This expository paper introduces several ideas in chromatic homotopy theory around Morava's extraordinary E-theories. In particular, we construct various moduli problems closely related to Lubin-Tate deformation theory and study their symmetries. These symmetries are then used in conjunction with the Hopkins-Kuhn-Ravenel character theory to provide formulas for the power operations and the stabilizer group action on the E-cohomology of a finite group.

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Section: A Theorem Of Ando-hopkins-stricklandmentioning

confidence: 99%

Lubin-Tate theory, character theory, and power operations

Stapleton¹

2020

Handbook of Homotopy Theory

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“…SinceĚ * (BΣ p + ) is a finitely generated free E * -module and concentrated in even degrees, we have a duality isomorphism [30,Theorem 3.2]:…”

Section: Power Operations In Morava E-theorymentioning

confidence: 99%

On a nilpotence conjecture of J. P. May

2015

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Abstract. We prove a conjecture of J.P. May concerning the nilpotence of elements in ring spectra with power operations, i.e., H∞-ring spectra. Using an explicit nilpotence bound on the torsion elements in K(n)-local H∞-algebras over En, we reduce the conjecture to the nilpotence theorem of Devinatz, Hopkins, and Smith. As corollaries we obtain nilpotence results in various bordism rings including M Spin * and M String * , results about the behavior of the Adams spectral sequence for E∞-ring spectra, and the non-existence of E∞-ring structures on certain complex oriented ring spectra.

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“…In Section 3, based on calculations of E * BΣ m in [Str98] as reflected in the formula for S 3 , we define individual power operations, and derive the relations they satisfy. In view of the general structures studied in [Rez09], we then get an explicit description of the Dyer-Lashof algebra Γ for K(2)-local commutative E -algebras.…”

Section: Outline Of the Papermentioning

confidence: 99%