We construct a natural transformation from the Bousfield-Kuhn functor evaluated on a space to the Topological André-Quillen cohomology of the K ( n )-local Spanier–Whitehead dual of the space, and show that the map is an equivalence in the case where the space is a sphere. This results in a method for computing unstable $$v_n$$ v n -periodic homotopy groups of spheres from their Morava E -cohomology (as modules over the Dyer-Lashof algebra of Morava E -theory). We relate the resulting algebraic computations to the algebraic geometry of isogenies between Lubin–Tate formal groups.

中文翻译：

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Bousfield-Kuhn 函子和拓扑 André-Quillen 上同调

我们构建了从在空间上评估的 Bousfield-Kuhn 函子到空间的 K ( n )-局部 Spanier-Whitehead 对偶的拓扑 André-Quillen 上同调的自然变换，并表明该映射在以下情况下是等价的：空间是一个球体。这产生了一种从它们的 Morava E 上同调（作为 Morava E 理论的 Dyer-Lashof 代数上的模块）计算不稳定的 $$v_n$$ vn 球体周期性同伦群的方法。我们将由此产生的代数计算与 Lubin-Tate 形式群之间的同构性的代数几何相关联。