We revisit the computation, due to Hesselholt and Madsen, of the K-theory of truncated polynomial algebras for perfect fields of positive characteristic. The resulting K-groups are expressed in terms of big Witt vectors of the field. The original proof relied on an understanding of cyclic polytopes in order to determine the genuine equivariant homotopy type of the cyclic bar construction for a suitable monoid. Using the Nikolaus-Scholze framework for topological cyclic homology we achieve the same result using only the homology of said cyclic bar construction, as well as the action of Connes' operator.

中文翻译：

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关于截断多项式代数的 K 理论，重新审视

由于 Hesselholt 和 Madsen，我们重新计算了截断多项式代数的 K 理论，用于正特性的完美域。得到的 K 群用场的大 Witt 向量表示。最初的证明依赖于对环状多胞体的理解，以确定合适的幺半群的环状杆结构的真正等变同伦类型。将 Nikolaus-Scholze 框架用于拓扑循环同源性，我们仅使用所述循环杆构造的同源性以及 Connes 算子的作用就可以实现相同的结果。