论文标题
较弱的前观，派生的完成，ADIC平坦和棱镜
Weak Proregularity, Derived Completion, Adic Flatness, and Prisms
论文作者
论文摘要
本文有两个部分。在第一部分中，我们回想起重要的作用，即在派生的完成和ADIC平坦度中，理想中理想的前牙性弱弱。我们还介绍了理想主义和顺序派生的完成的新概念，并证明了一些结果，包括这两个概念同意如果理想是弱的。 在第二部分中，我们研究了弱核的局部性质及其行为W.R.T.戒指商。这些结果使我们能够证明，在Bhatt和Scholze的意义上，存在弱的核能发生在有限的棱镜的背景下。我们预料到，弱发现的概念将有助于简化和改善完美环和棱镜的开创性理论（近年来改变算术几何形状）。
This paper has two parts. In the first part we recall the important role that weak proregularity of an ideal in a commutative ring has in derived completion and in adic flatness. We also introduce the new concepts of idealistic and sequential derived completion, and prove a few results about them, including the fact that these two concepts agree iff the ideal is weakly proregular. In the second part we study the local nature of weak proregularity, and its behavior w.r.t. ring quotients. These results allow us to prove that weak proregularity occurs in the context of bounded prisms, in the sense of Bhatt and Scholze. We anticipate that the concept of weak proregularity will help simplify and improve some of the more technical aspects of the groundbreaking theory of perfectoid rings and prisms (that has transformed arithmetic geometry in recent years).
