The Tate spectrum of $v_{n}$ -periodic complex oriented theories

Greenless, J.P.C.; Sadofsky, Hal

doi:10.1007/pl00004264

Cited by 31 publications

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“…by using the factC 1 is K(1)-local. The vanishing of the Tate construction in the K(1)-local category [GS96] and Corollary 2.9 imply that…”

Section: From E-theory To K-theorymentioning

confidence: 95%

A transchromatic proof of Strickland's theorem

Schlank¹,

Stapleton²

2015

Advances in Mathematics

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In [Str98] Strickland proved that the Morava E-theory of the symmetric group has an algebro-geometric interpretation after taking the quotient by a certain transfer ideal. This result has influenced most of the work on power operations in Morava E-theory and provides an important calculational tool. In this paper we give a new proof of this result as well as a generalization by using transchromatic character theory. The character maps are used to reduce Strickland's result to representation theory.

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“…by using the factC 1 is K(1)-local. The vanishing of the Tate construction in the K(1)-local category [GS96] and Corollary 2.9 imply that…”

Section: From E-theory To K-theorymentioning

confidence: 95%

A transchromatic proof of Strickland's theorem

Schlank¹,

Stapleton²

2015

Advances in Mathematics

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“…The following theorem is due to Hovey-Sadofsky [HS96] in the K(n)-local case, and was strengthened by Kuhn [Kuh04b] to the T (n)-local case (see also [MS88], [GS96], and [CM17]).…”

Section: N -Periodic Homotopy Theorymentioning

confidence: 99%

Spectral Algebra Models of Unstable $$v_n$$-Periodic Homotopy Theory

Behrens

Rezk

2020

Bousfield Classes and Ohkawa's Theorem

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We give a survey of a generalization of Quillen-Sullivan rational homotopy theory which gives spectral algebra models of unstable vn-periodic homotopy types. In addition to describing and contextualizing our original approach, we sketch two other recent approaches which are of a more conceptual nature, due to Arone-Ching and Heuts. In the process, we also survey many relevant concepts which arise in the study of spectral algebra over operads, including topological André-Quillen cohomology, Koszul duality, and Goodwillie calculus.Date: May 29, 2017. Models of "unstable homotopy theory"The approach to unstable homotopy theory we are considering fits into a general context, which we will now describe.

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“…Transfer maps It follows from a result of Greenlees and Sadofsky [GS96] that there are transfer maps in E-cohomology along all maps of finite groups. In [Gan06, Section 7.3], Ganter studies the case of the transfer from G to the trivial group and shows that there is a simple formula for the transfer on the level of class functions.…”

Section: Toolsmentioning

confidence: 99%