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Title: A study on anabelian geometry of higher local fields
Authors: MUROTANI, Takahiro
Author's alias: 室谷, 岳寛
Keywords: 11S20
anabelian geometry
complete discrete valuation field
Grothendieck conjec- ture
higher local field
hyperbolic curve
Kummer-faithful field
mono-anabelian reconstruction
Issue Date: Mar-2021
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 20
Thesis number: RIMS-1944
Abstract: 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 the present paper, we consider this problem for higher local fields. First, to consider "anabelianness" of higher local fields themselves, we give mono-anabelian re-construction 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.
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Appears in Collections:Research Institute for Mathematical Sciences, preprints

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