关于K理论中的曲线和TR
On curves in K-theory and TR
摘要：
我们证明了TR是corepresentable的约化拓扑霍赫希尔德同调调的平坦仿射直线$\mathbf{S}[t]$作为一个函子定义的$\infty$ -类别的分圆谱与值的$\infty$ -类别的谱与Frobenius升降机，完善的结果Blumberg-Mandell。我们定义的概念，一个整体拓扑卡地亚模块使用巴维克的形式主义的光谱麦基函子的轨道$\infty$ -类别，扩展的工作Antieau尼古拉在$p$ -典型的设置。作为一个应用，我们表明，TR评估的连接$\mathbf{E}_1$ -环承认的频谱曲线的代数K理论的描述，推广工作的Hesselholt和Betley-Schlichtkrull。
英文摘要：
We prove that TR is corepresentable by the reduced topological Hochschild homology of the flat affine line $\mathbf{S}[t]$ as a functor defined on the $\infty$-category of cyclotomic spectra with values in the $\infty$-category of spectra with Frobenius lifts, refining a result of Blumberg-Mandell. We define the notion of an integral topological Cartier module using Barwick's formalism of spectral Mackey functors on orbital $\infty$-categories, extending the work of Antieau-Nikolaus in the $p$-typical setting. As an application, we show that TR evaluated on a connective $\mathbf{E}_1$-ring admits a description in terms of the spectrum of curves on algebraic K-theory generalizing the work of Hesselholt and Betley-Schlichtkrull.
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