完美oids阿比扬卡尔引理的一个变种与几乎Cohen-Macaulay代数
A variant of perfectoid Abhyankar's lemma and almost Cohen-Macaulay algebras
AI总结：
本文证明了混合特征下完备局部域的整闭几乎Cohen-Macaulay域的整延伸，并建立了完美环分解的Witt-完美版本的阿比扬卡尔引理和黎曼扩展定理。
摘要：
在本文中，我们证明了一个混合特征$p>0$的完备诺特局部域具有一个整闭、几乎Cohen-Macaulay域的整延伸，使得Frobenius映射对$p$可微。这一结果被视为正特征下完备局部域的完美闭包几乎Cohen-Macaulay的混合特征类比。为此，我们详细研究了完美环的分解以及建立了安德烈的完美oids阿比扬卡尔引理和黎曼扩展定理的Witt-完美（分解后的）版本。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
