Title: The spectral Sullivan conjecture Show Chinese title

Title: 谱Sullivan猜想

Abstract: We show that any map from an infinite loop space to a $p$-complete nilpotent finite dimensional space factors canonically through a union of $p$-adic tori. This is proven via bootstrapping from the case of $B\mathbb{Z}/p\mathbb{Z}$, which is the key case of the Sullivan conjecture proven by Miller. The main step in our proof is to show that the subcategory of spectra generated by the reduced suspension spectrum of $B\mathbb{Z}/p\mathbb{Z}$ under colimits and extensions agrees with that of a Moore spectrum. Show Chinese abstract

Abstract: 我们证明，从无限循环空间到$p$-完备的幂零有限维空间的任何映射都可以通过一个$p$-进环面的并集进行规范分解。 这是通过从$B\mathbb{Z}/p\mathbb{Z}$的情况进行自举来证明的，这是 Miller 证明的 Sullivan 猜想的关键情况。 我们证明的主要步骤是表明，由$B\mathbb{Z}/p\mathbb{Z}$的约化悬垂谱在余极限和扩张下生成的谱子范畴与一个 Moore 谱的子范畴一致。