论文标题
G-Global同义理论和代数K理论
G-Global Homotopy Theory and Algebraic K-Theory
论文作者
论文摘要
我们开发了$ g $ - 全球同型理论的基础，这是一方面的经典均等同质理论的综合，另一方面是全球同质理论。然后，我们介绍了$ g $ -Global代数$ K $ - 与$ g $ -Action的小型对称单相类型的理论，统一$ g $ - equivariant equivariant代数$ k $ - 理论，例如Shimakawa和Shimakawa和Schwede的全球Algebraic $ K $ - $ - $ - $ - $ - $ - $ - - 作为理论的应用，我们证明$ g $ -Global代数$ K $ - 理论函子以$ G $ - action的类别为类别，作为$ g $ -ACTION作为连接$ g $ g $ g $ global稳定同质理论的模型，由于经典的非估计性成果，托马斯儿的普遍化和增强。这特别使我们能够推断出全球和e象代数$ k $ - 理论的相应语句。
We develop the foundations of $G$-global homotopy theory as a synthesis of classical equivariant homotopy theory on the one hand and global homotopy theory in the sense of Schwede on the other hand. Using this framework, we then introduce the $G$-global algebraic $K$-theory of small symmetric monoidal categories with $G$-action, unifying $G$-equivariant algebraic $K$-theory, as considered for example by Shimakawa, and Schwede's global algebraic $K$-theory. As an application of the theory, we prove that the $G$-global algebraic $K$-theory functor exhibits the category of small symmetric monoidal categories with $G$-action as a model of connective $G$-global stable homotopy theory, generalizing and strengthening a classical non-equivariant result due to Thomason. This in particular allows us to deduce the corresponding statements for global and equivariant algebraic $K$-theory.
