主题片段和彩色操作
Motivic slices and colored operads
摘要：
着色运算是在20世纪70年代为了研究拓扑空间上的同伦不变量代数结构而引入的。本文在动机稳定同伦理论中引入了色算子。我们的主要动机是揭示迄今未知的高度结构化的性质的切片过滤。后者将每个动机谱分解成它的切片，这些切片是动机，人们可能会问切片过滤在多大程度上保留了高度结构化的对象，如代数和模块。我们使用有色操作数来精确地解决这个问题。我们的方法利用公理化的设置，专门为经典和motivic稳定同伦理论。可解释的t-结构是一般理论发展的核心。简明介绍了有色操作和Bousfield（co）本地化在单独的附录。
英文摘要：
Colored operads were introduced in the 1970's for the purpose of studying homotopy invariant algebraic structures on topological spaces. In this paper we introduce colored operads in motivic stable homotopy theory. Our main motivation is to uncover hitherto unknown highly structured properties of the slice filtration. The latter decomposes every motivic spectrum into its slices, which are motives, and one may ask to what extend the slice filtration preserves highly structured objects such as algebras and modules. We use colored operads to give a precise solution to this problem. Our approach makes use of axiomatic setups which specialize to classical and motivic stable homotopy theory. Accessible t-structures are central to the development of the general theory. Concise introductions to colored operads and Bousfield (co)localizations are given in separate appendices.
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