论文标题
$ k $的模块结构 - 多项式戒指的理论
Module structure of the $K$-theory of polynomial-like rings
论文作者
论文摘要
假设$γ$是一个晶格的下monoid，不包含一条线。在本说明中，我们在Monoid代数$ r [γ] $上使用天然$γ$分类来证明有关相对$ k $ - 理论$ k（r [γ]，r）$的结构性结果。当$ r $包含一个字段时，我们证明了射线索引的分解为$γ$，而witt vectors $ r $的兼容动作对于每种$ \ mathbf n $ - $γ$。在特征零中，Witt向量还针对截断设置$γ$还有一项动作。最后，我们将其应用于$ k _*（r [x_1，...，...，x_n]）$ j。\，戴维斯提出的$。
Suppose $Γ$ is a submonoid of a lattice, not containing a line. In this note, we use the natural $Γ$-grading on the monoid algebra $R[Γ]$ to prove structural results about the relative $K$-theory $K(R[Γ], R)$. When $R$ contains a field, we prove a decomposition indexed by the rays in $Γ$, and a compatible action by the Witt vectors of $R$ for each $\mathbf N$-grading of $Γ$. In characteristic zero, there is additionally an action by Witt vectors for the truncation set $Γ$. Finally, we apply this to get a ray-like description of $K_*(R[x_1,...,x_n])$ proposed by J.\,Davis.
