# 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.
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https://hal.archives-ouvertes.fr/hal-00944820
Contributor : Lionel Schwartz <>
Submitted on : Thursday, February 5, 2015 - 12:45:23 PM
Last modification on : Tuesday, May 5, 2020 - 1:03:21 PM
Document(s) archivé(s) le : Wednesday, May 6, 2015 - 10:16:25 AM

### Files

CGPS-fin.pdf
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### Identifiers

• 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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