论文标题
完美的Abhyankar的引理和几乎Cohen-Macaulay代数的一种变体
A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
论文作者
论文摘要
在本文中，我们证明了一个完整的Noetherian本地域，具有完美的残留场的混合特性$ P> 0 $具有一个积分的扩展名，它是一个积分封闭的，几乎是Cohen-Macaulay域，因此Frobenius Map是偏斜的Modulo $ P $。该结果被视为一个混合特征的类似物，即在积极特征中完整的局部领域的完美封闭几乎是科恩·马库拉（Cohen-Macaulay）。为此，我们进行了一项详细的研究，对完美环的年代化，并建立了安德烈（André）完美的abhyankar的引理和里曼（Riemann）的扩展定理的完美（重新完成）版本。
In this paper, we prove that a complete Noetherian local domain of mixed characteristic $p>0$ with perfect residue field has an integral extension that is an integrally closed, almost Cohen-Macaulay domain such that the Frobenius map is surjective modulo $p$. This result is seen as a mixed characteristic analogue of the fact that the perfect closure of a complete local domain in positive characteristic is almost Cohen-Macaulay. To this aim, we carry out a detailed study of decompletion of perfectoid rings and establish the Witt-perfect (decompleted) version of André's perfectoid Abhyankar's lemma and Riemann's extension theorem.
