# 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} }

## 133 Citations

Homotopy groups of homotopy fixed point spectra associated to En

- Mathematics
- 2007

2 for p> 2, where En is the Landweber exact spectrum whose coefficient ring is the ring of functions on the Lubin‐Tate moduli space of lifts of the height n Honda formal group law over Fpn , and Hn…

Homotopy fixed points for Lubin-Tate spectra

- Mathematics
- 2009

We construct a stable model structure on profinite symmetric spectra with a continuous action of an arbitrary profinite group. This provides a natural framework for the construction of homotopy fixed…

Buildings, elliptic curves, and the K (2)-local sphere

- Mathematics
- 2005

We investigate a dense subgroup Γ of the second Morava stabilizer group given by a certain group of quasi-isogenies of a supersingular elliptic curve in characteristic p. The group Γ acts on the…

CONTINUOUS HOMOTOPY FIXED POINTS FOR LUBIN-TATE SPECTRA

- Mathematics
- 2009

We provide a new and conceptually simplified construction of continuous homotopy fixed point spectra for Lubin-Tate spectra under the action of the extended Morava stabilizer group. Moreover, our new…

A Lyndon-Hochschild-Serre spectral sequence for certain homotopy fixed point spectra

- Mathematics
- 2004

Let H and K be closed subgroups of the extended Morava stabilizer group G n and suppose that H is normal in K. We construct a strongly convergent spectral sequence H* c (K/H,(E h n H )*X) ⇒ (E h n K…

The cohomology of the height four Morava stabilizer group at large primes

- Mathematics
- 2016

This is an announcement of some new computational methods in stable homotopy theory, in particular, methods for using the cohomology of small-height Morava stabilizer groups to compute the cohomology…

Morava K-theory and Filtrations by Powers

- Mathematics
- 2021

We prove the convergence of the Adams spectral sequence based on Morava Ktheory and relate it to the filtration by powers of the maximal ideal in the Lubin–Tate ring through a Miller square. We use…

PROFINITE G-SPECTRA

- Mathematics
- 2013

We construct a stable model structure on profinite spectra with a continuous action of an arbitrary profinite group. The motivation is to provide a natural framework in a subsequent paper for a new…

Moduli stack of oriented formal groups and periodic complex bordism

- Mathematics
- 2021

We introduce and study the non-connective spectral stack M FG, the moduli stack of oriented formal groups. We realize some results of chromatic homotopy theory in terms of the geometry of this stack.…

## References

SHOWING 1-10 OF 42 REFERENCES

Invertible Spectra in the E(n)‐Local Stable Homotopy Category

- Mathematics
- 1999

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

- Mathematics
- 1998

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

- Mathematics
- 1977

? 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

- Mathematics
- 2000

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.

- Mathematics
- 1972

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…

On relations between Adams spectral sequences, with an application to the stable homotopy of a moore space

- Mathematics
- 1981

THE LOCALIZATION OF SPECTRA WITH RESPECT TO HOMOLOGY

- Mathematics
- 2001

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

- Mathematics
- 1993

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…