Une résolution projective pour le second groupe de Morava pour p ≥ 5 et applications

Olivier Lader 1
1 Algèbre, topologie, groupes quantiques, représentations
IRMA - Institut de Recherche Mathématique Avancée
Abstract : In the 80's, Shimomura has computed the homotopy groups of the Moore spectrum V(0) localized with respect to Morava K-theory K(2). Some years later, Devinatz and Hopkins found an other spectral sequence converging to those homotopy groups. When the prime paramater p of K(2) is greather or equal to five, the preceding spectral collapses. Thus, computing those homotopy groups consists in computing the cohomology groups of Morava Stabilizer Group with coefficients in the Lubin-Tate ring mod p. In 2007, Henn has showed that there exists, when p >3, a projective resolution of the Morava stabilizer group of length four. In this thesis, we give a more precise description of this resolution. Then, we use it for the computation of the cohomology groups of Morava Stabilizer Group with coefficients in the Lubin-Tate ring mod p. As a second application, we give an other proof of the unpublished result of Hopkins on the Picard group of the K(2)-local spectrum category.
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Olivier Lader. Une résolution projective pour le second groupe de Morava pour p ≥ 5 et applications. Topologie algébrique [math.AT]. Université de Strasbourg, 2013. Français. ⟨NNT : 2013STRAD028⟩. ⟨tel-00875761⟩

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