A_inf的一些环论性质
Some ring-theoretic properties of A_inf
摘要：
特征为p的完备赋值环上的维特向量环，通常记为A_inf，在p进霍奇理论中起着关键作用;例如，Bhatt、Morrow和Scholze最近通过将其与某个A_inf值上同调理论联系起来，重新解释和改进了晶体比较同构。我们解决了一些基本的环理论问题的A_inf的动机与二维正则局部环的类比。例如，我们表明，在大多数情况下，A_inf，这显然不是诺特，也不是连贯的。另一方面，它确实有一个性质，即Spec A_inf中闭点的补上的向量丛确实唯一地在穿刺上延伸;此外，类似的陈述在Huber的adic空间范畴中也成立。
英文摘要：
The ring of Witt vectors over a perfect valuation ring of characteristic p, often denoted A_inf, plays a pivotal role in p-adic Hodge theory; for instance, Bhatt, Morrow, and Scholze have recently reinterpreted and refined the crystalline comparison isomorphism by relating it to a certain A_inf-valued cohomology theory. We address some basic ring-theoretic questions about A_inf motivated by analogies with two-dimensional regular local rings. For example, we show that in most cases A_inf, which is manifestly not noetherian, is also not coherent. On the other hand, it does have the property that vector bundles over the complement of the closed point in Spec A_inf do extend uniquely over the puncture; moreover, a similar statement holds in Huber's category of adic spaces.
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