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SOME REMARKS ON PROFINITE COMPLETION OF SPACES
"... Abstract. We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of ArtinMazur and Sullivan which extends also to nonconnected spaces. Another new aspect is an equivariant profinite completion functor and equivari ..."
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Abstract. We study profinite completion of spaces in the model category of profinite spaces and construct a rigidification of the completion functors of ArtinMazur and Sullivan which extends also to nonconnected spaces. Another new aspect is an equivariant profinite completion functor and equivariant fibrant replacement functor for a profinite group acting on a space. This is crucial for applications where, for example, Galois groups are involved, or for profinite Teichmüller theory where equivariant completions are applied. Along the way we collect and survey the most important known results about profinite completion of spaces. 1.
TORSION ALGEBRAIC CYCLES AND ÉTALE COBORDISM
"... Abstract. We prove that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of ℓadic étale cobordism over an algebraically closed field of positive characteristic. This shows that there is a strong topological obstruction for cohomology classe ..."
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Abstract. We prove that the classical integral cycle class map from algebraic cycles to étale cohomology factors through a quotient of ℓadic étale cobordism over an algebraically closed field of positive characteristic. This shows that there is a strong topological obstruction for cohomology classes to be algebraic and that examples of Atiyah, Hirzebruch and Totaro also work in positive characteristic. 1.
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 ..."
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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 homotopy fixed point spectral sequences for LubinTate spectra under the action of the extended Morava stabilizer group.