论文标题
合格的$ s $ -s-algebra模块理论：一些工具和示例
Homotopy theory of modules over a commutative $S$-algebra: some tools and examples
论文作者
论文摘要
现代类别的光谱类别，例如配备了严格对称的单体粉碎产品的Elmendorf等人的光谱类别，允许引入对称单体，从而提供了一种研究高度连贯的交通便当环光谱的新方法。这些具有类别的模块，这些模块是对相对于球体光谱模块的经典类别的概括。传递到他们的派生或同型类别会导致可以探索同质理论的新环境。在本文中，我们描述了一些可用于研究这些“勇敢的新同质理论”的工具，并通过考虑$ k $ - 理论频谱的模块来证明它们，这些模块与Mahowald的$ bo $ resolutions Theorys密切相关。在计划的续集中，我们将把这些技术应用于拓扑模块形式的$ 2 $局部结缔范围内的不太熟悉的模块上下文。
Modern categories of spectra such as that of Elmendorf et al equipped with strictly symmetric monoidal smash products allows the introduction of symmetric monoids providing a new way to study highly coherent commutative ring spectra. These have categories of modules which are generalisations of the classical categories of spectra that correspond to modules over the sphere spectrum; passing to their derived or homotopy categories leads to new contexts in which homotopy theory can be explored. In this paper we describe some of the tools available for studying these `brave new homotopy theories' and demonstrate them by considering modules over the $K$-theory spectrum, closely related to Mahowald's theory of $bo$-resolutions. In a planned sequel we will apply these techniques to the much less familiar context of modules over the $2$-local connective spectrum of topological modular forms.
