A study on anabelian geometry of higher local fields
A study on anabelian geometry of higher local fields
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高等局域场阿贝尔几何的研究
DOI：
10.1142/s1793042123500604
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发表时间：
2023
影响因子：
0.7
通讯作者：
Murotani Takahiro
中科院分区：
文献类型：
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作者：
吉本 将隆;清水 啓佑;鈴木 耕太;田村 和久;菅野 了次;平山 雅章;Murotani Takahiro
Anabelian几何已经发展了一个更广泛的领域比Grothendieck，谁是Anabelian几何的创始人，示意图。因此，很自然地会问这样一个问题：什么样的场适合于阿那贝尔几何的基场？在本文中，我们考虑这个问题的高局部域。首先，考虑到高等局部域本身的“反阿贝尔性”，我们给出了高等局部域的各种不变量从其绝对伽罗瓦群的单反阿贝尔重构算法。因此，某些类型的高等局部域的同构类完全由它们的绝对伽罗瓦群决定。其次，我们证明了混合特征高阶局部域是Kummer-忠实的。这一结果在一定程度上证实了上述问题对于这些高局域场的适用性。
Anabelian geometry has been developed over a much wider class of fields than Grothendieck, who is the originator of anabelian geometry, conjectured. So, it is natural to ask the following question: What kinds of fields are suitable for the base fields of anabelian geometry?In this paper, we consider this problem for higher local fields. First, to consider “anabelianness” of higher local fields themselves, we give mono-anabelian reconstruction algorithms of various invariants of higher local fields from their absolute Galois groups. As a result, the isomorphism classes of certain types of higher local fields are completely determined by their absolute Galois groups. Next, we prove that mixed-characteristic higher local fields are Kummer-faithful. This result affirms the above question for these higher local fields to a certain extent.