论文标题
在代数$ k $ - 双点的理论
On The Algebraic $K$-Theory of Double Points
论文作者
论文摘要
在本文中，我们使用跟踪方法来研究$ r [x_1，\ ldots，x_d]/（x_1，\ ldots，x_d）^2 $的代数$ k $ - 表格的戒指理论。我们计算了相对$ p $ -adic $ k $ gubles for $ r $ a Perfectoid戒指。 In particular, we get the integral $K$ groups when $R$ is a finite field, and the integral relative $K$ groups $K_*(R[x_1,\ldots, x_d]/(x_1,\ldots, x_d)^2, (x_1,\ldots, x_d))$ when $R$ is a perfect $\mathbb{F}_p$-algebra.我们以其他一些值得注意的计算结束了论文，其中包括一些不完全是上述形式的环。
In this paper, we use trace methods to study the algebraic $K$-theory of rings of the form $R[x_1,\ldots, x_d]/(x_1,\ldots, x_d)^2$. We compute the relative $p$-adic $K$ groups for $R$ a perfectoid ring. In particular, we get the integral $K$ groups when $R$ is a finite field, and the integral relative $K$ groups $K_*(R[x_1,\ldots, x_d]/(x_1,\ldots, x_d)^2, (x_1,\ldots, x_d))$ when $R$ is a perfect $\mathbb{F}_p$-algebra. We conclude the paper with some other notable computations, including some rings which are not quite of the above form.
