论文标题
本地化不变的基本定理
The Fundamental Theorem of Localizing Invariants
论文作者
论文摘要
我们通过将代数k理论的证据扩展到稳定的$ \ infty $ - 类别的领域，来证明对Verdier-locatier jear的基础定理的概括。该公式对于Karoubi-localization函子，verdier-locatier的不变式的函数的表现要好得多。这种一般的基本定理专门针对非共同的K理论，拓扑Hochschild同源性和拓扑循环同源性以及任意环光谱的连接K理论，并概括了代数的几个已知公式，并将代数K理论概述了普通环或普通环和$ $ $ \ \ \ \ \ \ \ shembb的连接。
We prove a generalization of the fundamental theorem of algebraic K-theory for Verdier-localizing functors by extending the proof for algebraic K-theory of spaces to the realm of stable $\infty$-categories. The formula behaves much better for Karoubi-localizing functors, the Verdier-localizing invariants which are additionally invariant under idempotent completion. This general fundamental theorem specializes to new formulas in the context of non-connective K-theory, topological Hochschild homology and topological cyclic homology as well as connective K-theory of arbitrary ring spectra, and generalizes several known formulas for algebraic K-theory of spaces or connective K-theory of ordinary rings, schemes and $\mathbb{S}$-algebras.
