论文标题
H空间和高度1色均匀理论的K主理论
The K-theory cochains of H-spaces and height 1 chromatic homotopy theory
论文作者
论文摘要
修复一个奇怪的prime $ p $。令$ x $为一个尖的空间，其$ p $ completed k理论$ \ mathrm {ku} _p^*（x）$是有限数量的奇数生成器上的外部代数；示例包括奇数和许多H空间。我们给出了$ \ mathbf {e} _ \ infty $ - $ \ mathrm {ku} _p $ -Algebra spectrum $ \ mathrm {ku} _p^{x _ _ _ _ _ _++} $ $ \ \ m iartrm {为了促进这种结构，我们描述了$ \ mathrm {k}（1）$ - $ \ mathbf {e} _1 $ -ring Spectra的tor光谱序列的本地类似物。结合Bousfield的先前工作，对$ X $的Cochains的描述恢复了Kjaer的结果，即$ v_1 $ - 周期均匀的同型$ x $可以由这些Cochains建模。然后，这意味着高度的商誉塔1 Bousfield-Kuhn Foundor以这种$ x $收敛。
Fix an odd prime $p$. Let $X$ be a pointed space whose $p$-completed K-theory $\mathrm{KU}_p^*(X)$ is an exterior algebra on a finite number of odd generators; examples include odd spheres and many H-spaces. We give a generators-and-relations description of the $\mathbf{E}_\infty$-$\mathrm{KU}_p$-algebra spectrum $\mathrm{KU}_p^{X_+}$ of $\mathrm{KU}_p$-cochains of $X$. To facilitate this construction, we describe a $\mathrm{K}(1)$-local analogue of the Tor spectral sequence for $\mathbf{E}_1$-ring spectra. Combined with previous work of Bousfield, this description of the cochains of $X$ recovers a result of Kjaer that the $v_1$-periodic homotopy type of $X$ can be modelled by these cochains. This then implies that the Goodwillie tower of the height 1 Bousfield-Kuhn functor converges for such $X$.
