Small ring spectra

Devinatz, Ethan S.

doi:10.1016/0022-4049(92)90131-x

Cited by 18 publications

(36 citation statements)

References 3 publications

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“…Since X ! F.EG C ; X / is a non-equivariant equivalence we conclude, using Equation (8)(9)(10)(11)(12), that X n and C n X are non-equivariant equivalent. Hence X n 2 D n for all…”

Section: An Example: Greenlees Connective K -Theorymentioning

confidence: 83%

“…Since X and Y are W -S -cell complexes, and a map from a compact space C into a W -S -cell complex factors through a finite sub cell complex, it suffices to verify the claim for individual cells. Recall, from (3)(4)(5)(6)(7)(8)(9)(10)(11)(12), that…”

Section: Fibrationsmentioning

confidence: 99%

“…There exists a U 2 W such that the map from j to f .V / L factors through f .V / UL . Since f .V / UL is a fibration we get a lift in the diagram (4)(5)(6)(7)(8)(9)(10)(11)(12)(13)(14)(15)(16)(17)(18). Hence f .V / L is a fibration.…”

Section: Fibrationsmentioning

confidence: 99%

“…(1) The finite p -local spectra M I constructed by Devinatz assemble to give an interesting pro-spectrum fM I g [12]. The pro-spectrum is more well behaved than the individual spectra.…”

Section: Examples Of Pro-g -Spectramentioning

confidence: 99%

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Equivariant homotopy theory for pro–spectra

Fausk

2008

Geom. Topol.

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We extend the theory of equivariant orthogonal spectra from finite groups to profinite groups, and more generally from compact Lie groups to compact Hausdorff groups. The G -homotopy theory is "pieced together" from the G=U -homotopy theories for suitable quotient groups G=U of G ; a motivation is the way continuous group cohomology of a profinite group is built out of the cohomology of its finite quotient groups. In the model category of equivariant spectra Postnikov towers are studied from a general perspective. We introduce pro-G -spectra and construct various model structures on them. A key property of the model structures is that pro-spectra are weakly equivalent to their Postnikov towers. We discuss two versions of a model structure with "underlying weak equivalences". One of the versions only makes sense for pro-spectra. In the end we use the theory to study homotopy fixed points of pro-G -spectra. 55P91; 18G55

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“…Since X ! F.EG C ; X / is a non-equivariant equivalence we conclude, using Equation (8)(9)(10)(11)(12), that X n and C n X are non-equivariant equivalent. Hence X n 2 D n for all…”

Section: An Example: Greenlees Connective K -Theorymentioning

confidence: 83%

Section: Fibrationsmentioning

confidence: 99%

Section: Fibrationsmentioning

confidence: 99%

“…(1) The finite p -local spectra M I constructed by Devinatz assemble to give an interesting pro-spectrum fM I g [12]. The pro-spectrum is more well behaved than the individual spectra.…”

Section: Examples Of Pro-g -Spectramentioning

confidence: 99%

See 2 more Smart Citations

Equivariant homotopy theory for pro–spectra

Fausk

2008

Geom. Topol.

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“…These spectra do not exist for all sequences i, but they do exist for a cofinal set of sequences, and Devinatz has shown [4] that there is a cofinal collection all of which are ring spectra. These spectra are not determined by the sequence, but it follows from the Nilpotence Theorem that they are asymptotically unique in the sense that hocolim i M i is independent of all choices.…”

Section: Localization Away From Ideals and Bousfield Localizationmentioning

confidence: 99%