论文标题
DP-FINITE FIELDS IV：等级2图片
Dp-finite fields IV: the rank 2 picture
论文作者
论文摘要
我们研究了特征0和DP级别2的字段。尽管我们没有获得分类，但我们证明了任何特征性0和DP级别2的不稳定领域都可以接受独特的可定义V-Topology。如果可以将此陈述推广到较高的等级，我们将获得有限DP级领域的预期分类。 通过研究早期工作中定义的“规范拓扑”，我们获得了独特的可定义V-Topology。与早期的期望相反，规范拓扑不必是V-Topology。但是，我们能够根据差异值字段来表征规范拓扑（在DP级2和特征0）中。 这种差异性结构是通过对“ 2-流动器”的部分分类获得的，这是一种自然在有限等级的领域中产生的广义评估。 此外，我们举例说明了ACVF的DP级2扩展，具有一组完整的等级和空内部。这个示例干扰了证明Henselianity猜想的某些策略。
We investigate fields of characteristic 0 and dp-rank 2. While we do not obtain a classification, we prove that any unstable field of characteristic 0 and dp-rank 2 admits a unique definable V-topology. If this statement could be generalized to higher ranks, we would obtain the expected classification of fields of finite dp-rank. We obtain the unique definable V-topology by investigating the "canonical topology" defined in earlier work. Contrary to earlier expectations, the canonical topology need not be a V-topology. However, we are able to characterize the canonical topology (on fields of dp-rank 2 and characteristic 0) in terms of differential valued fields. This differential valued structure is obtained through a partial classification of "2-inflators," a sort of generalized valuation that arises naturally in fields of finite rank. Additionally, we give an example of a dp-rank 2 expansion of ACVF with a definable set of full rank and empty interior. This example interferes with certain strategies for proving the henselianity conjecture.
