### Citations

500 |
Homotopy limits, completions and localizations
- Bousfield, Kan
- 1972
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Citation Context ...Z → Zf is a weak equivalence with Zf fibrant. Also, “holim” always denotes the version of the homotopy limit of spectra that is constructed levelwise in the category of simplicial sets, as defined in =-=[2]-=- and [22, 5.6]. In Section 2, for a finite group G, we use the fact that the homotopy colimit of a diagram of pointed simplicial sets is the diagonal of the simplicial replacement of the diagram, to o... |

459 | An introduction to homological algebras, - Weibel - 1994 |

308 | Simplicial Homotopy Theory, - Goerss, Jardine - 1999 |

140 | Equivariant Homotopy and Cohomology Theory. - May - 1996 |

101 | Morava K-theories and localisation - Hovey, Strickland - 1999 |

101 | Profinite groups - Ribes, Zalesskii - 2000 |

98 | Analytic pro-p groups - Dixon, Sautoy, et al. - 1991 |

91 | The localization of spectra with respect to homology, - Bousfield - 1979 |

63 |
Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups”, Topology 43
- Devinatz, Hopkins
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Citation Context ...zer group, where Sn is the nth Morava stabilizer group, and recall that the profinite group Gn is compact `-adic analytic. By work of Paul Goerss, Mike Hopkins, and Haynes Miller (see [18], [10], and =-=[6]-=-), the group Gn acts on En. Now let K(n) be the nth Morava K-theory, with K(n)∗ = F`[v±1n ], where the degree of vn is 2(`n−1). Also, let LK(n)(−) denote the Bousfield localization functor with respec... |

46 |
Notes on the Hopkins-Miller theorem. In Homotopy theory via algebraic geometry and group representations
- Rezk
- 1997
(Show Context)
Citation Context ...d Morava stabilizer group, where Sn is the nth Morava stabilizer group, and recall that the profinite group Gn is compact `-adic analytic. By work of Paul Goerss, Mike Hopkins, and Haynes Miller (see =-=[18]-=-, [10], and [6]), the group Gn acts on En. Now let K(n) be the nth Morava K-theory, with K(n)∗ = F`[v±1n ], where the degree of vn is 2(`n−1). Also, let LK(n)(−) denote the Bousfield localization func... |

40 | Algebraic K-theory and étale cohomology - Thomason - 1985 |

37 | A resolution of the K(2)-local sphere at the prime 3 - Goerss, Henn, et al. |

37 | Generalized étale cohomology theories - Jardine - 1997 |

32 | Moduli Spaces of Commutative Ring Spectra
- Goerss, Hopkins
- 2004
(Show Context)
Citation Context ...va stabilizer group, where Sn is the nth Morava stabilizer group, and recall that the profinite group Gn is compact `-adic analytic. By work of Paul Goerss, Mike Hopkins, and Haynes Miller (see [18], =-=[10]-=-, and [6]), the group Gn acts on En. Now let K(n) be the nth Morava K-theory, with K(n)∗ = F`[v±1n ], where the degree of vn is 2(`n−1). Also, let LK(n)(−) denote the Bousfield localization functor wi... |

32 | Hypercohomology spectra and Thomason’s descent theorem. Algebraic K-theory - Mitchell - 1996 |

20 | Homotopy fixed points for LK(n)(En ∧ X) using the continuous action
- Davis
(Show Context)
Citation Context ... way to try to do this fails. Let EdhNin be the spectrum constructed by Devinatz and Hopkins (see [6]) that behaves like the Ni-homotopy fixed points of En with respect to a continuous Ni-action (see =-=[4]-=-). Let MI0 ←MI1 ←MI2 ← · · · be a tower of generalized Moore spectra such that holim j (LK(n)(MIj ))f ' LK(n)(S0) ([13, Proposition 7.10 (e)]). Also, recall from [4, Theorem 6.6] that En ' holim j (co... |

19 | A Lyndon-Hochschild-Serre spectral sequence for certain homotopy fixed point spectra - Devinatz - 2005 |

18 |
Pontrjagin duality for generalized homology and cohomology theories,
- Comenetz
- 1976
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Citation Context ...the function spectrum itself is fibrant. These facts imply that the spectrum holimi F ((XNi)c, Zf) is an S[[G]]-module. We give two examples of F (X,Z) as an S[[G]]-module. Example 4.2. Recall from =-=[3]-=- that, if cS0 is the Brown-Comenetz dual of S0, then cX, the Brown-Comenetz dual of X, is F (X, cS0). Thus, if X is a discrete right G-spectrum, then cX = holim i F ((XNi)c, (cS0)f) is an S[[G]]-modul... |

16 | Cohomology of p-adic analytic groups. - Symonds, Weigel - 2000 |

15 | Equivariant homotopy theory for pro-spectra, Geom
- Fausk
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Citation Context ... above spectral sequence to identify the spectrum F (En, LK(n)(S0))hGn more concretely is work in progress. We want to point out that others have investigated homotopy orbits for profinite groups. In =-=[8]-=-, Halvard Fausk studies homotopy orbits in the setting of proorthogonal G-spectra, where G is profinite. As pointed out in various places in this paper, Mark Behrens has worked on homotopy orbits for ... |

12 | Profinite groups. The Clarendon - Wilson - 1998 |

9 | Gross-Hopkins duality - Strickland |

7 |
Generalised sheaf cohomology theories. Axiomatic, enriched and motivic homotopy theory, 29{68
- Jardine
- 2004
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Citation Context ...et A[−n] be the chain complex that is A in degree n and zero elsewhere. Given the tower {Ai}, we explain how to form {H(Ai)}, a tower of EilenbergMac Lane spectra (we follow the construction given in =-=[15]-=-), so that holimiH(Ai) is an S[[G]]-module. By functoriality, for each k ≥ 0, {Γ(Ai[−k])} is a tower of simplicial G-modules and G-equivariant maps, such that, for each i, Γ(Ai[−k]) is the Eilenberg-M... |