论文标题
代数K理论中的参数化非交通动机和均等立方下降
Parametrised noncommutative motives and equivariant cubical descent in algebraic K-theory
论文作者
论文摘要
对于Barwick-Dotto-Glasman-Nardin-Shah的意义上的原子轨道基础类别，我们介绍了参数化的完美稳定类别的类别，并使用它来构建代数K理论的非合并动机的参数性版本，其中核心是核心的。此外，我们启动了一种具有独立感兴趣的参数立方的基本理论，它概括了多托（Dotto）在e象案例之外的dotto equivariant gotwillie colculus中的某些元素。使用这种立方体理论，我们表明，在有限的2组G的均衡情况下，参数化的非交通动机在规范上精炼了G-符号对称单类类别。因此，这赋予了这些群体的模棱两可的代数K理论光谱，其结构是在山丘 - 霍普金斯 - 雷诺尔（Hill-Hopkins-Ravenel）的意义上配备了乘法规范的E-Infinity光谱。在此过程中，我们还将提供一台机器来制造来自配备G acTions的对称单类别的G-对称单类别类别，并阐明上述参数式的完美稳定类别与与完美稳定类别中有价值的Mackey Fuctors相关的方式。
For an atomic orbital base category in the sense of Barwick-Dotto-Glasman-Nardin-Shah, we introduce the category of parametrised perfect-stable categories and use it to construct the parametrised version of noncommutative motives in which algebraic K-theory is corepresented. Furthermore, we initiate a rudimentary theory of parametrised cubes which could be of independent interest, generalising some of the elements in Dotto's theory of equivariant Goodwillie calculus beyond the equivariant case. Using this cubical theory, we show that in the equivariant case for finite 2-groups G, the parametrised noncommutative motives canonically refine to G-symmetric monoidal categories. Consequently, this endows the equivariant algebraic K-theory spectra for these groups with the structure of E-infinity-ring spectra equipped with multiplicative norms in the sense of Hill-Hopkins-Ravenel. Along the way, we will also provide a machine to manufacture G-symmetric monoidal categories from symmetric monoidal categories equipped with G-actions and elucidate how the aforementioned parametrised perfect-stable categories relate to Mackey functors valued in perfect-stable categories.
