Geodesic
The topological Singer construction
Documenta mathematica, Tome 17 (2012), pp. 861-909
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We study the continuous (co-)homology of towers of spectra, with emphasis on a tower with homotopy inverse limit the Tate construction XtG on a G-spectrum X. When G=Cp​ is cyclic of prime order and X=B∧p is the p-th smash power of a bounded below spectrum B with H∗​(B;Fp​) of finite type, we prove that (B∧p)tCp​ is a topological model for the Singer construction R+​(H∗(B;Fp​)) on H∗(B;Fp​). There is a stable map εB​:B→(B∧p)tCp​ inducing the ExtA​-equivalence ε:R+​(H∗(B;Fp​))→H∗(B;Fp​). Hence εB​ and the canonical map Γ:(B∧p)Cp​→(B∧p)hCp​ are p-adic equivalences.
DOI : 10.4171/dm/384
Classification : 55P42, 55P91, 55S10, 55T15
Mots-clés : singer construction, Tate construction, limit of Adams spectral sequences, \( \Ext \)-equivalence 
@article{10_4171_dm_384,
     author = {Sverre Lun{\o}e-Nielsen and John Rognes},
     title = {The topological {Singer} construction},
     journal = {Documenta mathematica},
     pages = {861--909},
     year = {2012},
     volume = {17},
     doi = {10.4171/dm/384},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/dm/384/}
}
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Sverre Lunøe-Nielsen; John Rognes. The topological Singer construction. Documenta mathematica, Tome 17 (2012), pp. 861-909. doi: 10.4171/dm/384

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