论文标题
$ k $ - 内态理论，$ \ mathit {tr} $ - trace和zeta函数
$K$-theory of endomorphisms, the $\mathit{TR}$-trace, and zeta functions
论文作者
论文摘要
我们表明，特征多项式和lefschetz zeta函数是从$ k $ - 内态理论到拓扑限制同源性（TR）的痕量图的表现。一路上，我们将Lindenstrauss和McCarthy的地图从$ K $ - 内态理论概述到拓扑限制同源性，为任何Waldhausen类别定义了与正交光谱中兼容的富集定义。特别是，这将它们的构造从环扩展到环光谱。我们还对原始的Dennis Trace Map进行了修正主义者的处理，从$ K $ - 理论到拓扑Hochschild同源性（THH），并解释其与Shadow（也称为Trace Theeories）的生物游戏中的痕迹的联系。
We show that the characteristic polynomial and the Lefschetz zeta function are manifestations of the trace map from the $K$-theory of endomorphisms to topological restriction homology (TR). Along the way we generalize Lindenstrauss and McCarthy's map from $K$-theory of endomorphisms to topological restriction homology, defining it for any Waldhausen category with a compatible enrichment in orthogonal spectra. In particular, this extends their construction from rings to ring spectra. We also give a revisionist treatment of the original Dennis trace map from $K$-theory to topological Hochschild homology (THH) and explain its connection to traces in bicategories with shadow (also known as trace theories).
