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ファイル | 記述 | サイズ | フォーマット | |
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RIMS1974.pdf | 552.74 kB | Adobe PDF | 見る/開く |
タイトル: | Resolution of Nonsingularities, Point-theoreticity, and Metric-admissibility for p-adic Hyperbolic Curves |
著者: | MOCHIZUKI, Shinichi TSUJIMURA, Shota |
キーワード: | 14H30 14H25 anabelian geometry resolution of nonsingularities absolute Grothendieck Conjecture combinatorial anabelian geometry Grothendieck-Teichmüller group étale fundamental group tempered fundamental group hyperbolic curve configuration space |
発行日: | Jun-2023 |
出版者: | Research Institute for Mathematical Sciences Kyoto University |
開始ページ: | 1 |
終了ページ: | 107 |
論文番号: | RIMS-1974 |
抄録: | In this paper, we prove that arbitrary hyperbolic curves over p-adic local fields admit resolution of nonsingularities [“RNS”]. This result may be regarded as a generalization of results concerning resolution of nonsingularities obtained by A. Tamagawa and E. Lepage. Moreover, by combining our RNS result with techniques from combinatorial anabelian geometry, we prove that an absolute version of the geometrically pro-Σ Grothendieck Conjecture for arbitrary hyperbolic curves over p-adic local fields, where Σ denotes a set of prime numbers of cardinality ≥ 2 that contains p, holds. This settles one of the major open questions in anabelian geometry. Furthermore, we prove --again by applying RNS and combinatorial anabelian geometry-- that the various p-adic versions of the Grothendieck-Teichmüller group that appear in the literature in fact coincide. As a corollary, we conclude that the metrized Grothendieck-Teichmüller group is commensurably terminal in the Grothendieck-Teichmüller group. This settles a longstanding open question in combinatorial anabelian geometry. |
URI: | http://hdl.handle.net/2433/284398 |
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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