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Pré-Publication, Document De Travail Année : 2014

Around conjectures of N. Kuhn

Résumé

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.
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Dates et versions

hal-00944820 , version 1 (11-02-2014)
hal-00944820 , version 2 (06-01-2015)
hal-00944820 , version 3 (05-02-2015)

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Citer

Nguyen The Cuong, Gérald Gaudens, Geoffrey Powell, Lionel Schwartz. Around conjectures of N. Kuhn. 2014. ⟨hal-00944820v2⟩
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