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2003 Espaces profinis et problèmes de réalisabilité
Francois-Xavier Dehon, Gerald Gaudens
Algebr. Geom. Topol. 3(1): 399-433 (2003). DOI: 10.2140/agt.2003.3.399


The mod p cohomology of a space comes with an action of the Steenrod Algebra. L. Schwartz [A propos de la conjecture de non realisation due a N. Kuhn, Invent. Math. 134, No 1, (1998) 211–227] proved a conjecture due to N. Kuhn [On topologicaly realizing modules over the Steenrod algebra, Annals of Mathematics, 141 (1995) 321–347] stating that if the mod p cohomology of a space is in a finite stage of the Krull filtration of the category of unstable modules over the Steenrod algebra then it is locally finite. Nevertheless his proof involves some finiteness hypotheses. We show how one can remove those finiteness hypotheses by using the homotopy theory of profinite spaces introduced by F. Morel [Ensembles profinis simpliciaux et interpretation geometrique du foncteur T, Bull. Soc. Math. France, 124 (1996) 347–373], thus obtaining a complete proof of the conjecture. For that purpose we build the Eilenberg–Moore spectral sequence and show its convergence in the profinite setting.


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Francois-Xavier Dehon. Gerald Gaudens. "Espaces profinis et problèmes de réalisabilité." Algebr. Geom. Topol. 3 (1) 399 - 433, 2003.


Received: 29 November 2002; Revised: 3 May 2003; Accepted: 14 January 2003; Published: 2003
First available in Project Euclid: 21 December 2017

zbMATH: 1022.55012
MathSciNet: MR1997324
Digital Object Identifier: 10.2140/agt.2003.3.399

Primary: 55S10
Secondary: 55T20, 57T35

Rights: Copyright © 2003 Mathematical Sciences Publishers


Vol.3 • No. 1 • 2003
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