论文标题
结构化环光谱TQ完成的纤维定理
Fibration theorems for TQ-completion of structured ring spectra
论文作者
论文摘要
这份简短论文的目的是在适当条件下建立Bousfield-Kan“纤维化引理”的光谱代数类似物。我们在代数结构的背景下工作，可以将其描述为对称光谱中的Operad $ \ Mathcal {O} $的代数。我们的主要结果是，关于拓扑Quillen同源性（或简称TQ-Completion）的完成保留了同型纤维化序列，规定连接了基础和总$ \ Mathcal {O} $ - 代数。我们的论点本质上归结为证明了从同质纤维到其TQ-Completion塔的自然图是$ $π_*$同构。更普遍地，我们还表明，如果我们用“同型回调方形”替换“同型纤维化序列”，那么相似的结果仍然是正确的。
The aim of this short paper is to establish a spectral algebra analog of the Bousfield-Kan "fibration lemma" under appropriate conditions. We work in the context of algebraic structures that can be described as algebras over an operad $\mathcal{O}$ in symmetric spectra. Our main result is that completion with respect to topological Quillen homology (or TQ-completion, for short) preserves homotopy fibration sequences provided that the base and total $\mathcal{O}$-algebras are connected. Our argument essentially boils down to proving that the natural map from the homotopy fiber to its TQ-completion tower is a pro-$π_*$ isomorphism. More generally, we also show that similar results remain true if we replace "homotopy fibration sequence" with "homotopy pullback square."
