参数化非交换动机与代数K-理论中的共变立方降维
Parametrised noncommutative motives and equivariant cubical descent in algebraic K-theory
AI总结：
本文引入参数化完美稳定范畴，构建参数化非交换动机，研究其在有限2群上的共变结构，揭示其与Mackey函子的关系。
摘要：
对于Barwick-Dotto-Glasman-Nardin-Shah意义下的原子轨道基础范畴，我们引入参数化完美稳定范畴，并用其构造参数化非交换动机，其中代数K-理论被核心表示。进一步，我们启动参数化立方的初步理论，扩展Dotto的共变Goodwillie微分学。利用此立方理论，我们证明在有限2群G的共变情况下，参数化非交换动机自然细化为G-对称单子范畴。因此，这使这些群的共变代数K-理论谱获得E-infinity环谱结构，并配备Hill-Hopkins-Ravenel意义下的乘法规范。同时，我们还将提供一种机器，从带有G作用的对称单子范畴制造G-对称单子范畴，并阐述上述参数化完美稳定范畴如何与Mackey函子相关联。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
