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Une description fonctorielle des K-théories de Morava des 2-groupes abéliens élémentaires

Abstract : The aim of this PhD thesis is to study, from a functorial point of view, the mod 2 Morava K-theories of elementary abelian 2-groups. Namely, we study the covariant functors V \mapsto K(n)^*(BV^{\sharp}) for the prime p=2 and n a positive integer. The case n=1, which follows directly from the work of Atiyah on topological K-theory, gives us a coanalytic functor which contains no non-constant polynomial sub-functor. This is very different from the case n>1, where the above-mentioned functors are analytic. The theory of Henn-Lannes-Schwartz provides a correspondence between analytic functors and unstable modules over the Steenrod algebra. We determine the unstable module corresponding to the analytic functor V \mapsto K(2)^*(BV^{\sharp}), by studying the relation between this functor and the Hopf ring structure of the homology of the omega-spectrum associated to the theory K(2).
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Submitted on : Friday, March 2, 2018 - 12:17:08 PM
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  • HAL Id : tel-01565626, version 2

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Le Chi Quyet Nguyen. Une description fonctorielle des K-théories de Morava des 2-groupes abéliens élémentaires. Topologie algébrique [math.AT]. Université d'Angers, 2017. Français. ⟨NNT : 2017ANGE0032⟩. ⟨tel-01565626v2⟩

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