# Around conjectures of N. Kuhn

Abstract : We discuss two extensions of results conjectured by Nick Kuhn about the non-realization of unstable algebras as the mod $p$ singular cohomology of a space, for $p$ a prime. The first extends and refines earlier work of the second and fourth authors, using Lannes' mapping space theorem. The second (for the prime $2$) is based on an analysis of the $-1$ and $-2$ columns of the Eilenberg-Moore spectral sequence, and of the associated extension. In both cases, the statements and proofs use the relationship between the categories of unstable modules and functors between $\Fp$-vector spaces. The second result in particular exhibits the power of the functorial approach.
keyword :
Type de document :
Pré-publication, Document de travail
2014

https://hal.archives-ouvertes.fr/hal-00944820
Contributeur : Lionel Schwartz <>
Soumis le : jeudi 5 février 2015 - 12:45:23
Dernière modification le : mercredi 6 février 2019 - 01:23:49
Document(s) archivé(s) le : mercredi 6 mai 2015 - 10:16:25

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CGPS-fin.pdf
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### Identifiants

• HAL Id : hal-00944820, version 3
• ARXIV : 1402.2617

### Citation

Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz. Around conjectures of N. Kuhn. 2014. 〈hal-00944820v3〉

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