Espaces profinis et problemes de realisabilite
| Autor: | Gérald Gaudens, Francois-Xavier Dehon |
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| Rok vydání: | 2003 |
| Předmět: |
Pure mathematics
Conjecture Steenrod algebra realization Homotopy nilpotent modules profinite spaces Space (mathematics) Mathematics::Algebraic Topology Cohomology Action (physics) Eilenberg–Moore spectral sequence Mathematics::K-Theory and Homology Spectral sequence Steenrod operations 55S10 55T20 57T35 Filtration (mathematics) FOS: Mathematics 57T35 Algebraic Topology (math.AT) Geometry and Topology Mathematics - Algebraic Topology 55S10 55T20 Mathematics |
| Zdroj: | Algebr. Geom. Topol. 3, no. 1 (2003), 399-433 |
| DOI: | 10.48550/arxiv.math/0306271 |
| Popis: | 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. Comment: Published by Algebraic and Geometric Topology at http://www.maths.warwick.ac.uk/agt/AGTVol3/agt-3-13.abs.html |
| Databáze: | OpenAIRE |
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