ダウンロード数: 92
このアイテムのファイル:
ファイル | 記述 | サイズ | フォーマット | |
---|---|---|---|---|
RIMS1944.pdf | 172.3 kB | Adobe PDF | 見る/開く |
タイトル: | A study on anabelian geometry of higher local fields |
著者: | MUROTANI, Takahiro |
著者名の別形: | 室谷, 岳寛 |
キーワード: | 11S20 14G20 14h30 anabelian geometry complete discrete valuation field Grothendieck conjec- ture higher local field hyperbolic curve Kummer-faithful field mono-anabelian reconstruction |
発行日: | Mar-2021 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
開始ページ: | 1 |
終了ページ: | 20 |
論文番号: | RIMS-1944 |
抄録: | 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. |
URI: | http://hdl.handle.net/2433/262333 |
関連リンク: | http://www.kurims.kyoto-u.ac.jp/preprint/index.html |
出現コレクション: | 数理解析研究所プレプリント |
このリポジトリに保管されているアイテムはすべて著作権により保護されています。