Results 1  10
of
457
THE HOMOTOPY ORBIT SPECTRUM FOR PROFINITE GROUPS
"... Abstract. Let G be a profinite group. We define an S[[G]]module to be a Gspectrum X that satisfies certain conditions, and, given an S[[G]]module X, we define the homotopy orbit spectrum XhG. When G is countably based and X satisfies a certain finiteness condition, we construct a homotopy orbit s ..."
Abstract
 Add to MetaCart
Abstract. Let G be a profinite group. We define an S[[G]]module to be a Gspectrum X that satisfies certain conditions, and, given an S[[G]]module X, we define the homotopy orbit spectrum XhG. When G is countably based and X satisfies a certain finiteness condition, we construct a homotopy orbit
The homotopy fixed point spectra of profinite Galois extensions
"... Let E be a klocal profinite GGalois extension of an E∞ring spectrum A (in the sense of Rognes). We show that E may be regarded as producing a discrete Gspectrum. Also, we prove that if E is a profaithful klocal profinite extension which satisfies certain extra conditions, then the forward dir ..."
Abstract

Cited by 22 (15 self)
 Add to MetaCart
direction of Rognes’s Galois correspondence extends to the profinite setting. We show the function spectrum FA((EhH)k, (EhK)k) is equivalent to the homotopy fixed point spectrum ((E[[G/H]]) hK)k where H and K are closed subgroups of G. Applications to Morava Etheory are given, including showing
CONTINUOUS GROUP ACTIONS ON PROFINITE SPACES
"... Abstract. For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point spaces and for stable homotopy groups of homotopy orbit spaces. Our main example ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
Abstract. For a profinite group, we construct a model structure on profinite spaces and profinite spectra with a continuous action. This yields descent spectral sequences for the homotopy groups of homotopy fixed point spaces and for stable homotopy groups of homotopy orbit spaces. Our main example
Profinite Homotopy Theory
 DOCUMENTA MATH.
, 2008
"... We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and prospaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy g ..."
Abstract

Cited by 6 (3 self)
 Add to MetaCart
We construct a model structure on simplicial profinite sets such that the homotopy groups carry a natural profinite structure. This yields a rigid profinite completion functor for spaces and prospaces. One motivation is the étale homotopy theory of schemes in which higher profinite étale homotopy
PROFINITE AND DISCRETE GSPECTRA AND ITERATED HOMOTOPY FIXED POINTS
"... Abstract. In chromatic homotopy theory, given K ⊳ G < Gn, closed subgroups of the extended Morava stabilizer group Gn, and the LubinTate spectrum En, which carries an action by Gn, the problem of understanding both the homotopy fixed point spectra of En for the actions of K and G and the relatio ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
Abstract. In chromatic homotopy theory, given K ⊳ G < Gn, closed subgroups of the extended Morava stabilizer group Gn, and the LubinTate spectrum En, which carries an action by Gn, the problem of understanding both the homotopy fixed point spectra of En for the actions of K and G
Iterated homotopy fixed points for the LubinTate spectrum
, 2006
"... When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not always possible to form the iterated homotopy fixed point spectrum (ZhH) hK/H, where Z is a continuous Gspectrum. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = ̂ L(En ∧ X ..."
Abstract

Cited by 12 (9 self)
 Add to MetaCart
When G is a profinite group and H and K are closed subgroups, with H normal in K, it is not always possible to form the iterated homotopy fixed point spectrum (ZhH) hK/H, where Z is a continuous Gspectrum. However, we show that, if G = Gn, the extended Morava stabilizer group, and Z = ̂ L
PROFINITE GSPECTRA
 HOMOLOGY, HOMOTOPY AND APPLICATIONS, VOL. 15(1), 2013, PP.151–189
, 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 and conceptually simplified construction of continuous homotopy fixed point spectra and of continuous ..."
Abstract

Cited by 1 (0 self)
 Add to MetaCart
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 and conceptually simplified construction of continuous homotopy fixed point spectra and of continuous
The homotopy groups of the spectrum Tmf
, 2012
"... We use the structure of the homotopy groups of the connective spectrum tmf of topological modular forms and the elliptic and AdamsNovikov spectral sequences to compute the homotopy groups of the nonconnective version Tmf of that spectrum. This is done separately for the localizations at 2, 3 and h ..."
Abstract
 Add to MetaCart
We use the structure of the homotopy groups of the connective spectrum tmf of topological modular forms and the elliptic and AdamsNovikov spectral sequences to compute the homotopy groups of the nonconnective version Tmf of that spectrum. This is done separately for the localizations at 2, 3
COCYCLE SUPERRIGIDITY FOR PROFINITE ACTIONS OF PROPERTY (T) GROUPS
, 2008
"... Consider a free ergodic measure preserving profinite action Γ � X (i.e. an inverse limit of actions Γ � Xn, with Xn finite) of a countable property (T) group Γ (more generally of a group Γ which admits an infinite normal subgroup Γ0 such that the inclusion Γ0 ⊂ Γ has relative property (T) and Γ/Γ0 i ..."
Abstract

Cited by 28 (3 self)
 Add to MetaCart
Consider a free ergodic measure preserving profinite action Γ � X (i.e. an inverse limit of actions Γ � Xn, with Xn finite) of a countable property (T) group Γ (more generally of a group Γ which admits an infinite normal subgroup Γ0 such that the inclusion Γ0 ⊂ Γ has relative property (T) and Γ/Γ0
Results 1  10
of
457