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Sur l'action des coopérations homologiques sur l'homologie de Brown-Peterson de l'espace classifiant d'un p-groupe abélien élémentaire

Abstract : Let p be a prime, n an integer, V an elementary abelian p-group of rank n and E a commutative, complex-oriented Landweber exact ring spectrum. The goal of this work is to study the comodule structure of the E-homology of BV over the Hopf algebroid (E_*,E_*E). To do this, we study localisation fonctors on comodule categories and the semi-direct product of Hopf algebroids. In the case where E is the Brown-Peterson spectrum BP, Johnson and Wilson have exhibited a filtration of the BP-homology of BZ/p^n in the category of BP_*-modules. We prove an analogous result in the category of BP_*BP-comodules; the filtration quotients depend on the universal p-series. In order to carry out explicit calculations, we introduce a Hopf algebroid (S,S\Lambda) which represents the groupoid associated to the action by conjugation of strict formal series on all formal series.
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https://tel.archives-ouvertes.fr/tel-00608646
Contributor : Sylvain Rairat <>
Submitted on : Wednesday, July 13, 2011 - 4:31:14 PM
Last modification on : Tuesday, October 20, 2020 - 3:56:17 PM
Long-term archiving on: : Monday, November 12, 2012 - 11:05:58 AM

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  • HAL Id : tel-00608646, version 1

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Sylvain Rairat. Sur l'action des coopérations homologiques sur l'homologie de Brown-Peterson de l'espace classifiant d'un p-groupe abélien élémentaire. Mathématiques [math]. Université Paris-Nord - Paris XIII, 2011. Français. ⟨tel-00608646⟩

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