论文标题
在混合特征的完整本地环中关闭操作
Closure operations in complete local rings of mixed characteristic
论文作者
论文摘要
Extended Plus（EPF）闭合和等级1（R1F）关闭是Raymond C. Heitmann引入的两个封闭操作，用于混合特征。最近，他和Linquan MA证明，EPF闭合在轻度条件下满足了通常的结肠捕获特性。在本文中，我们扩展了他们的结果，并证明EPF关闭满足了我们所谓的$ P $ -Colon捕获物业。基于此，我们定义了一个新的封闭概念，称为“弱EPF闭合”，并证明它满足了广义的结肠捕获特性和其他一些结肠捕获的特性。这给出了新的证据，证明了混合特征案例中存在大型科恩·麦克劳莱代数。我们还表明，完整局部域的任何模块 - 限制延伸是EPF-Phantom，它概括了Mel Hochster和Craig Huneke关于“ Phantom Extensions”的结果。最后，我们证明了特征$ p $的一些相关结果。
Extended plus (epf) closure and rank 1 (r1f) closure are two closure operations introduced by Raymond C. Heitmann for rings of mixed characteristic. Recently, he and Linquan Ma proved that epf closure satisfies the usual colon-capturing property under mild conditions. In this paper, we extend their result and prove that epf closure satisfies what we call the $p$-colon-capturing property. Based on that, we define a new closure notion called "weak epf closure", and prove that it satisfies the generalized colon-capturing property and some other colon-capturing properties. This gives a new proof of the existence of big Cohen-Macaulay algebras in the mixed characteristic case. We also show that any module-finite extension of a complete local domain is epf-phantom, which generalizes a result of Mel Hochster and Craig Huneke about "phantom extensions". Finally, we prove some related results in characteristic $p$.
