论文标题
积分扩展的差异模块的局部协同学II
Local Cohomology of Module of Differentials of Integral Extensions II
论文作者
论文摘要
在本说明中（$ r，m $）表示一个完整的常规本地戒指，$ b $主要表示其绝对积分封闭。本文的四个目标如下：i）确定$ω__{b/r} $的最高最高的当地同谋$ 0 $，ii），以在$ω__{b/r} $和$ω__{b/r v} $和$ω____________________________________________________________________________________________________________________________________________________________{b/v} $上进行a/v}混合特征中的同子学，其中$ v $是$ r $和$ a $的系数环，是其绝对不可或缺的关闭，iii），以证明可以将$ω__{b/r} $映射到共同体上的cohen-macaulay模块上，以便研究$/v} $ cohen-macaulay and iv） $ c $是一个积分域和$ r $的模块有限扩展。在这方面，已经完成了铃木定理关于在所有特征中正式设置的完整交叉点的正态性的扩展。
In this note ($R, m$) denotes a complete regular local ring and $B$ mostly denotes its absolute integral closure. The four objectives of this paper are the following: i) to determine the highest non-vanishing local cohomology of $Ω_{B/R}$ in equicharacteristic $0$, ii) to establish a connection between each of $Ω_{B/R}$ and $Ω_{B/V}$ and pull-back of $Ω_{A/V}$ via a short exact sequence together with new observations on corresponding local cohomologies in mixed characteristic where $V$ is the coefficient ring of $R$ and $A$ is its absolute integral closure, iii) to demonstrate that $Ω_{B/R}$ can be mapped onto a cohomologically Cohen-Macaulay module and iv) to study torsion-free property for $Ω_{C/V}$ and $Ω_{C/k}$ along with their respective completions where $C$ is an integral domain and a module finite extension of $R$. In this connection an extension of Suzuki's theorem on normality of complete intersections to the formal set-up in all characteristics is accomplished.
