Morava’s change of rings theorem

Devinatz, Ethan S.

doi:10.1090/conm/181/02031

Cited by 26 publications

(48 citation statements)

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“…This is known to be true and is a change of rings result; see [34] §15 for the exact analog of this result in the elliptic case. See also [11] for a similar result in the formal case.…”

Section: The Realization Problemmentioning

confidence: 54%

“…Note that on a traditional Adams spectral sequence chart, where the axes are (t − s, s), the non-zero groups of Theorem 2.5.1 appear in odd columns and odd rows -a kind of modified "checkerboard" pattern. 11 Thus we immediately have that the obstruction groups 2.5 vanish and the spectral sequence at the end of section 2.3 collapses, except possibly for differentials beginning with…”

Section: ) There Is An Isomorphismmentioning

confidence: 90%

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(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

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In the first part of this article, I will state a realization problem for diagrams of structured ring spectra, and in the second, I will discuss the moduli space which parametrizes the problem.While some of what I say is quite general, the ring spectra I have in mind will arise from the chromatic point of view, which uses the geometry of formal groups to organize stable homotopy theory. Thus, a subsidiary aim here is to reemphasize this connection between algebraic geometry and homotopy theory.

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“…This is known to be true and is a change of rings result; see [34] §15 for the exact analog of this result in the elliptic case. See also [11] for a similar result in the formal case.…”

Section: The Realization Problemmentioning

confidence: 54%

Section: ) There Is An Isomorphismmentioning

confidence: 90%

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

Goerss¹

2004

Axiomatic, Enriched and Motivic Homotopy Theory

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“…By unraveling the definitions of these maps in [Dev95], it is clear that if g 2 S n is given by g D P 1 j D0 a j S j , and then…”

Section: 2mentioning

confidence: 99%

“…If X is a finite spectrum, Morava's theory ( [Mor85], also [Dev95]) provides an action of S n on E n X. Furthmore, Gal Á Gal.F p n =F p / acts on E n X via its action on W F p n , making E n X into a G n -module, where G n Á S n Ì Gal. In fact, this action is induced by an action (in the stable homotopy category) of…”

mentioning

confidence: 99%

The Smith-Toda complexV((p+ 1)∕2) does not exist

Nave¹

2010

Ann. Math.

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“…as a semi-direct product K C 3 . Note that every element of order three in S 1 2 maps to a nonzero element in C 3 so that K is torsion free.…”

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confidence: 99%

A resolution of the K(2)-local sphere at the prime 3

et al. 2005

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We develop a framework for displaying the stable homotopy theory of the sphere, at least after localization at the second Morava K-theory K(2). At the prime 3, we write the spectrum L K(2) S 0 as the inverse limit of a tower of fibrations with four layers. The successive fibers are of the form E hF 2 where F is a finite subgroup of the Morava stabilizer group and E 2 is the second Morava or Lubin-Tate homology theory. We give explicit calculation of the homotopy groups of these fibers. The case n = 2 at p = 3 represents the edge of our current knowledge: n = 1 is classical and at n = 2, the prime 3 is the largest prime where the Morava stabilizer group has a p-torsion subgroup, so that the homotopy theory is not entirely algebraic.The problem of understanding the homotopy groups of spheres has been central to algebraic topology ever since the field emerged as a distinct area of mathematics. A period of calculation beginning with Serre's computation of the cohomology of Eilenberg-MacLane spaces and the advent of the Adams spectral sequence culminated, in the late 1970s, with the work of Miller, Ravenel, and Wilson on periodic phenomena in the homotopy groups of spheres and Ravenel's nilpotence conjectures. The solutions to most of these conjectures by Devinatz, Hopkins, and Smith in the middle 1980s established the primacy of the "chromatic" point of view and there followed a period in which the community absorbed these results and extended the qualitative picture of stable homotopy theory. Computations passed from center stage, to some extent, although there has been steady work in the wings

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Morava’s change of rings theorem

Cited by 26 publications

References 0 publications

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

(PRE-)Sheaves of Ring Spectra Over the Moduli Stack of Formal Group Laws

The Smith-Toda complexV((p+ 1)∕2) does not exist

A resolution of the K(2)-local sphere at the prime 3

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