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On the homotopy groups of the K(2)-localisation of a 2-local finite spectrum

Abstract : Let A1 be any spectrum in a class of finite spectra whose mod-2 cohomology is isomorphic to a free module of rank one over the subalgebra A(1) of the Steenrod algebra. Let EC be the second Morava-E theory associated to a universal deformation of the formal completion of the supersingular elliptic curve (C) : y2+y = x3 defined over F4 and S1C a certain closed subgroup of the Morava stabiliser group. As first steps towards understanding the homotopy type of the K(2)-localisation of the 2-local sphere spectrum, we analyse, in this thesis, the topological duality spectral sequence for EChS^1_C ^A1[symbol dollar], constructed by Irina Bobkova and Paul Goerss. In particular, we compute the E1-term of the latter and prove that its edge homomorphism is surjective.
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Submitted on : Wednesday, April 1, 2020 - 6:22:13 PM
Last modification on : Monday, October 12, 2020 - 1:33:06 PM


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Viet Cuong Pham. On the homotopy groups of the K(2)-localisation of a 2-local finite spectrum. K-Theory and Homology [math.KT]. Université de Strasbourg, 2019. English. ⟨NNT : 2019STRAD048⟩. ⟨tel-02374239v2⟩



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