论文标题
$ k $ - 截短的多项式理论
$K$-Theory of Truncated Polynomials
论文作者
论文摘要
我们研究代数$ k $ - 表格$ r [x]/x^e $的戒指理论。我们通过痕量方法和过滤对拓扑Hochschild同源性以及准脉络层均匀搁板的相关理论来做到这一点。我们就$ r $的大型矢量为$ r $ a $ $ r $制作了计算，就$ r $ $ r $的棱柱形曲线而言，$ r $ a $ a $ a $ a $平滑的曲线，以及$ r $ $ r $的混合特征的离散估值戒指，具有完美的残留戒指。
We study the algebraic $K$-theory of rings of the form $R[x]/x^e$. We do this via trace methods and filtrations on topological Hochschild homology and related theories by quasisyntomic sheaves. We produce computations for $R$ a perfectoid ring in terms of the big Witt vectors of $R$, for $R$ a smooth curve over a perfectoid ring in terms of the prismatic cohomology of $R$, and for $R$ a complete mixed characteristic discrete valuation rings with perfect residue field in terms of the prismatic cohomology and Hodge-Tate divisor of $R$.
