论文标题
关于$ \ infty $ - 类别和环形痕迹的nilpotent扩展
On nilpotent extensions of $\infty$-categories and the cyclotomic trace
论文作者
论文摘要
我们在本文中做了三件事：（1）研究本地化序列的类似物（在代数$ k $的意义上 - 稳定的$ \ infty $ - 类别的稳定$ \ infty $ - 类别），（（2）定义了适合$ \ iffty $ - \\ iffty extore的nilpotents and square square square square square square square square square square square square square square and（2） (1) and (2) to extend the Dundas-Goodwillie-McCarthy theorem for stable $\infty$-categories which are not monogenically generated (such as the stable $\infty$-category of Voevodsky's motives or the stable $\infty$-category of perfect complexes on some algebraic stacks).我们论文中的关键输入是邦托的重量结构概念，该概念提供了一个连接$ \ mathbb {e} _1 $ -ring Spectrum spectrum的“带有戒指”的类似物。作为应用程序，我们证明了CDH下降结果，用于将Hoyois-Krishna的工作扩展到同型$ k $ - 理论，并建立Blanc的晶格猜想的新案例。
We do three things in this paper: (1) study the analog of localization sequences (in the sense of algebraic $K$-theory of stable $\infty$-categories) for additive $\infty$-categories, (2) define the notion of nilpotent extensions for suitable $\infty$-categories and furnish interesting examples such as categorical square-zero extensions, and (3) use (1) and (2) to extend the Dundas-Goodwillie-McCarthy theorem for stable $\infty$-categories which are not monogenically generated (such as the stable $\infty$-category of Voevodsky's motives or the stable $\infty$-category of perfect complexes on some algebraic stacks). The key input in our paper is Bondarko's notion of weight structures which provides a "ring-with-many-objects" analog of a connective $\mathbb{E}_1$-ring spectrum. As applications, we prove cdh descent results for truncating invariants of stacks extending the work of Hoyois-Krishna for homotopy $K$-theory, and establish new cases of Blanc's lattice conjecture.
