Applications depuis K(Z/p,2) et une conjecture de Kuhn

Gérald Gaudens; Lionel Schwartz

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arXiv · 1004.5474

Applications depuis K(Z/p,2) et une conjecture de Kuhn

Gérald Gaudens·Lionel Schwartz

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Abstract

On démontre une conjecture due á N. Kuhn concernant la cohomologie singuliére á coefficients mod p des espaces, comme module instable sur l'algébre de Steenrod. Notre démonstration de ce résultat, déjá connu en caractéristique 2, fait appel á une m'ethode nouvelle, qui fonctionne en toute caracteristique. De cette maniére on rétablit un r'esultat de [S98] dont la preuve est incompléte dans le cas d'un nombre premier impair. ---- We settle a conjecture due to N. Kuhn about the mod p cohomology of spaces considered as unstable modules over the Steenrod algebra. This result is already known to hold in characteristic 2. The method presented here is essentially new and works for all characteristics. In doing so we fix a gap in [S98] concerning the odd prime case.

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Gérald Gaudens, Lionel Schwartz. 2010-05-25. Applications depuis K(Z/p,2) et une conjecture de Kuhn. https://arxiv.org/abs/1004.5474

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