We calculate the homotopy type of L1LK(2)S0and LK(1)LK(2)S0at the prime 2, where LK(n)is localization with respect to Morava K-theory and L1localization with respect to 2-local K theory. In L1LK(2)S0we find all the summands predicted by the Chromatic Splitting Conjecture, but we find some extra summands as well. An essential ingredient in our approach is the analysis of the continuous group cohomology H∗(G2,E0) where G2is the Morava stabilizer group and E0= W[[u1]] is the ring of functions on the height 2 Lubin-Tate space. We show that the inclusion of the constants W → E0induces an isomorphism on group cohomology, a radical simplification.
|Original language||English (US)|
|State||Published - Dec 21 2017|
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