Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups

@article{Devinatz2004HomotopyFP,
  title={Homotopy fixed point spectra for closed subgroups of the Morava stabilizer groups},
  author={Ethan S. Devinatz and Michael J. Hopkins},
  journal={Topology},
  year={2004},
  volume={43},
  pages={1-47}
}
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References

SHOWING 1-10 OF 42 REFERENCES
Invertible Spectra in the E(n)‐Local Stable Homotopy Category
Suppose C is a category with a symmetric monoidal structure, which we will refer to as the smash product. Then the Picard category is the full subcategory of objects which have an inverse under the
ON THE NONEXISTENCE OF SMITH-TODA COMPLEXES
Let p be a prime. The Smith-Toda complex V (k) is a nite spec- trum whose BP-homology is isomorphic to BP=(p;v1;:::;vk). For example, V ( 1) is the sphere spectrum and V (0) the mod p Moore spectrum.
E∞ ring spaces and E∞ ring spectra
? functors.- Coordinate-free spectra.- Orientation theory.- E? ring spectra.- On kO-oriented bundle theories.- E? ring spaces and bipermutative categories.- The recognition principle for E? ring
Cohomology of p-adic Analytic Groups
The purpose of this article is to give an exposition on the cohomology of compact p-adic analytic groups. The cohomology theory of profinite groups was initiated by J. Tate and developed by J-P.
Profinite Groups, Arithmetic, and Geometry.
In this volume, the author covers profinite groups and their cohomology, Galois cohomology, and local class field theory, and concludes with a treatment of duality. His objective is to present
THE LOCALIZATION OF SPECTRA WITH RESPECT TO HOMOLOGY
IN [8] WE studied localizations of spaces with respect to homology, and we now develop the analogous stable theory. Let Ho” denote the stable homotopy category of CW-spectra. We show that each
Bousfield Localization Functors and Hopkins' Chromatic Splitting Conjecture
This paper arose from attempting to understand Bousfield localization functors in stable homotopy theory. All spectra will be p-local for a prime p throughout this paper. Recall that if E is a
...
1
2
3
4
5
...