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Title: Anabelian geometry of complete discrete valuation fields and ramification filtrations
Authors: MUROTANI, Takahiro
Author's alias: 室谷, 岳寛
Keywords: 11S20
11S15
14G20
14H30
anabelian geometry
complete discrete valuation field
Grothendieck conjec- ture
hyperbolic curve
mono-anabelian reconstruction
ramification filtration
Issue Date: Mar-2021
Publisher: Research Institute for Mathematical Sciences, Kyoto University
Start page: 1
End page: 33
Thesis number: RIMS-1945
Abstract: As previous studies on anabelian geometry over p-adic local fields suggest, "ramifications of fields" play a key role in this area. In the present paper, more generally, we consider anabelian geometry of complete discrete valuation fields with perfect residue fields from the viewpoint of "ramifications of fields". Concretely, we establish mono-anabelian reconstruction algorithms of various invariants of these fields from their absolute Galois groups with ramification filtrations. By using these results, we reconstruct group-theoretically the isomorphism classes of mixed-characteristic complete discrete valuation fields with perfect residue fields under certain conditions. This result shows that these types of complete discrete valuation fields themselves have some "anabelianness". Moreover, we also investigate properties of homomorphisms between the absolute Galois groups of complete discrete valuation fields with perfect residue fields which preserve ramification filtrations.
Description: 本文ファイル(revision版)追加(2022/06/21)
URI: http://hdl.handle.net/2433/262334
Related Link: http://www.kurims.kyoto-u.ac.jp/preprint/index.html
Appears in Collections:Research Institute for Mathematical Sciences, preprints

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