# Continuous group actions on profinite spaces

```@article{Quick2009ContinuousGA,
title={Continuous group actions on profinite spaces},
author={Gereon Quick},
journal={Journal of Pure and Applied Algebra},
year={2009},
volume={215},
pages={1024-1039}
}```
• Gereon Quick
• Published 1 June 2009
• Mathematics
• Journal of Pure and Applied Algebra
26 Citations

### PROFINITE G-SPECTRA

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

### SOME REMARKS ON PROFINITE COMPLETION OF SPACES

We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of Artin-Mazur and Sullivan which extends also to

### CONTINUOUS HOMOTOPY FIXED POINTS FOR LUBIN-TATE SPECTRA

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

### Étale cohomology, purity and formality with torsion coefficients

• Mathematics
Journal of Topology
• 2022
We use Galois group actions on \'etale cohomology to prove results of formality for dg-operads and dg-algebras with torsion coefficients. Our theory applies, among other related constructions, to the

### The Fundamental Groupoid

We recall the fundamental groupoid of a connected, quasi-compact scheme X as in Grothendieck (Documents Mathematiques, vol. 3, 2003) Expose V, with special attention towards the effect of a

### Homotopy Rational Points of Brauer-Severi Varieties

We study homotopy rational points of Brauer-Severi varieties over fields of characteristic zero. We are particularly interested if a Brauer-Severi variety admitting a homotopy rational point splits.

### Sections, Homotopy Rational Points and Reductions of Curves

We study unramified sections of the fundamental group sequence of smooth projective curves of genus \$\geq 2\$ over \$p\$-adic fields together with an integral model. We are particularly interested in

## References

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### Profinite Homotopy Theory

We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite struc- ture. This yields a rigid profinite completion functor for spaces and

### Homotopy fixed points for Lubin-Tate spectra

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

### The real section conjecture and Smith's fixed‐point theorem for pro‐spaces

We prove a topological version of the section conjecture for the profinite completion of the fundamental group of finite CW‐complexes equipped with the action of a group of prime order p whose

### On finitely generated profinite groups, I: strong completeness and uniform bounds

• Mathematics
• 2006
We prove that in every finitely generated profinite group, every subgroup of finite index is open; this implies that the topology on such groups is determined by the algebraic structure. This is

### The local pro-p anabelian geometry of curves

Let X be a connected scheme. Then one can associate (after Grothendieck) to X its algebraic fundamental group π1(X). This group π1(X) is a profinite group which is uniquely determined (up to inner

### Equivariant stable homotopy and Sullivan's conjecture

Let G be a p-group, and let X be a G-complex. Let EG denote a contractible space on which G acts freely. By the "homotopy fixed point set" of X, we mean the fixed point set F(EG, X) G, where F(EG, X)