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ファイル | 記述 | サイズ | フォーマット | |
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RIMS1924.pdf | 292.32 kB | Adobe PDF | 見る/開く |
タイトル: | The Geometry of Hyperbolic Curvoids |
著者: | HOSHI, Yuichiro |
著者名の別形: | 星, 裕一郎 |
キーワード: | 14H30 hyperbolic curvoid hyperbolic curve anabelian geometry |
発行日: | Sep-2020 |
出版者: | Research Institute for Mathematical Sciences, Kyoto University |
開始ページ: | 1 |
終了ページ: | 46 |
論文番号: | RIMS-1924 |
抄録: | The main purposes of the present paper are to introduce the notion of a hyperbolic curvoid and to study the geometry of hyperbolic curvoids. A hyperbolic curvoid is defined to be a certain profinite group and may be considered to be "group-theoretic abstraction" of the notion of a hyperbolic curve from the viewpoint of anabelian geometry. One typical example of a hyperbolic curvoid is a profinite group isomorphic to the étale fundamental group of a hyperbolic curve either over a number field or over a mixed-characteristic nonarchimedean local field. The first part of the present paper centers around establishments of a construction of the "geometric subgroup" of hyperbolic curvoids and a construction of the "collection of cuspidal inertia subgroups" of hyperbolic curvoids. Moreover, we also consider respective analogues for hyperbolic curvoids of the theory of partial compactifications of hyperbolic curves and the theory of quotient orbicurves of hyperbolic curves by actions of finite groups. |
URI: | http://hdl.handle.net/2433/261822 |
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 |
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