Iterated homotopy fixed points for the Lubin–Tate spectrum

Davis, Daniel G.

doi:10.1016/j.topol.2009.08.026

Cited by 12 publications

(26 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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: 81%

“…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%

See 2 more Smart Citations

Equivariant homotopy theory for pro–spectra

Fausk

2008

Geom. Topol.

View full text Add to dashboard Cite

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

show abstract

“…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: 81%

Section: Fibrationsmentioning

confidence: 99%

See 1 more Smart Citation

Equivariant homotopy theory for pro–spectra

Fausk

2008

Geom. Topol.

View full text Add to dashboard Cite

show abstract

“…Much of this material overlaps with portions of [7]: it was necessary to repeat some of the material from [7], so that certain issues are clear and to give a context for the results of Section 7.1.…”

Section: Homotopy Fixed Points Of Discrete G-spectramentioning

confidence: 99%

The homotopy fixed point spectra of profinite Galois extensions

Behrens

Davis

2010

Trans. Amer. Math. Soc.

View full text Add to dashboard Cite

Abstract. Let E be a k-local profinite G-Galois extension of an E ∞ -ring spectrum A (in the sense of Rognes). We show that E may be regarded as producing a discrete G-spectrum. Also, we prove that if E is a profaithful k-local profinite extension which satisfies certain extra conditions, then the forward direction of Rognes's Galois correspondence extends to the profinite setting. We show that the function spectrum

show abstract

“…(see [1,Proposition 3.3.1] and [7,Theorem 3.4]). Thus, in general, the difficulties in forming the iterated homotopy fixed point spectrum occur only when H is a nontrivial non-open (closed normal) subgroup of K .…”

Section: An Overview Of Iterated Homotopy Fixed Points and The Problementioning

confidence: 99%

Delta-discreteG–spectra and iterated homotopy fixed points

Davis¹

2011

Algebr. Geom. Topol.

View full text Add to dashboard Cite

Let G be a profinite group with finite virtual cohomological dimension and let X be a discrete G -spectrum. If H and K are closed subgroups of G , with H C K , then, in general, the K=H -spectrum X hH is not known to be a continuous K=H -spectrum, so that it is not known (in general) how to define the iterated homotopy fixed point spectrum .X hH / hK =H . To address this situation, we define homotopy fixed points for delta-discrete G -spectra and show that the setting of delta-discrete G -spectra gives a good framework within which to work. In particular, we show that by using delta-discrete K=H -spectra, there is always an iterated homotopy fixed point spectrum, denoted

show abstract

Iterated homotopy fixed points for the Lubin–Tate spectrum

Cited by 12 publications

References 18 publications

Equivariant homotopy theory for pro–spectra

Equivariant homotopy theory for pro–spectra

The homotopy fixed point spectra of profinite Galois extensions

Delta-discreteG–spectra and iterated homotopy fixed points

Contact Info

Product

Resources

About