论文标题
追踪理论，Bokstedt周期性和bott becticities
Trace theories, Bokstedt periodicity and Bott periodicity
论文作者
论文摘要
我们充实了在Arxiv：1308.3743中概述的“跟踪理论”和“跟踪函数”的理论，将其扩展到同位词环境，并证明了重建定理，声称痕量理论完全由相关的跟踪函数确定。作为一个应用程序，我们考虑了代数$ a $ a $ a $ a $ a $ a $ a $的拓扑Hoshschild同源性$ thh（a，m），而在一个正面的正面特征上，其系数为bimodule $ m $，并证明了两个比较结果。首先，我们为Arxiv的Hochschild-Witt同源性提供了一个非常简单的代数模型：1604.01588（我们还使用定期版本$ WHP（a）$ WHH）确定了$ tp（a）$。其次，我们证明了$ thh（a）$被确定为共轭过滤的零期限，该期限是关于arXiv的共隔离环循环同源性$ \ of arxiv：1509.08784的$ \ overline {hp}（a）$，以及同构和同性恋派生的bokstedt周期性生成剂to the Botterator。我们还提供了Bokstedt周期性的独立证明，这比通常的周期性短一些。
We flesh out the theory of "trace theories" and "trace functors" sketched in arXiv:1308.3743, extend it to a homotopical setting, and prove a reconstruction theorem claiming that a trace theory is completely determined by the associated trace functor. As an application, we consider Topological Hoshschild Homology $THH(A,M)$ of a algebra $A$ over a perfect field of positive characteristic, with coefficients in a bimodule $M$, and prove two comparison results. Firstly, we give a very simple algebraic model for THH in terms of Hochschild-Witt Homology WHH of arXiv:1604.01588 (and we also identify $TP(A)$ with the periodic version $WHP(A)$ of WHH). Secondly, we prove that $THH(A)$ is identified with the zero term of the conjugate filtration on the co-periodic cyclic homology $\overline{HP}(A)$ of arXiv:1509.08784, and the isomorphism sends the Bokstedt periodicity generator to the Bott periodicity generator. We also give an independent proof of Bokstedt periodicity that is somewhat shorter than the usual ones.
