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The p-adic monodromy theorem in the imperfect residue field case
https://doi.org/10.15083/00005562
https://doi.org/10.15083/000055624de7159b-283b-4096-a9ed-9d8c6efe62e9
| 名前 / ファイル | ライセンス | アクション |
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OhkuboS_24_3_PhD_a.pdf (3.0 MB)
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OhkuboS_24_3_PhD_b.pdf (52.6 kB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-02-24 | |||||
| タイトル | ||||||
| タイトル | The p-adic monodromy theorem in the imperfect residue field case | |||||
| 言語 | ||||||
| 言語 | eng | |||||
| 資源タイプ | ||||||
| 資源 | http://purl.org/coar/resource_type/c_46ec | |||||
| タイプ | thesis | |||||
| ID登録 | ||||||
| ID登録 | 10.15083/00005562 | |||||
| ID登録タイプ | JaLC | |||||
| その他のタイトル | ||||||
| その他のタイトル | 剰余体が非完全な場合のp進モノドロミー定理について | |||||
| 著者 |
Ohkubo, Shun
× Ohkubo, Shun |
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| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 11600 | |||||
| 姓名 | 大久保, 俊 | |||||
| 著者所属 | ||||||
| 著者所属 | 東京大学大学院数理科学研究科 | |||||
| 著者所属 | ||||||
| 著者所属 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||
| Abstract | ||||||
| 内容記述タイプ | Abstract | |||||
| 内容記述 | Let K be a complete discrete valuation field of mixed characteristic (0, p) and GK the absolute Galois group of K. In this paper, we will prove the p-adic monodromy theorem for p-adic representations of GK without any assumption on the residue field of K, for example the finiteness of a p-basis of the residue field of K. The main point of the proof is a construction of (φ, GK)-module Ň(∇＋)(rig(V) for a de Rham representation V, which is a generalization of Pierre Colmez'Ň＋(rig)(V). In particular, our proof is essentially different from Kazuma Morita's proof in the case when the residue field admits a finite p-basis. We also give a few applications of the p-adic monodromy theorem, which are not mentioned in the literature. First, we prove a horizontal analogue of the p-adic monodromy theorem. Secondly, we prove an equivalence of categories between the category of horizontal de Rham representations of GK and the category of de Rham representations of an absolute Galois group of the canonical subfield of K. Finally, we compute H1 of some p-adic representations of GK, which is a generalization of Osamu Hyodo's results. | |||||
| 書誌情報 | 発行日 2012-03-22 | |||||
| 日本十進分類法 | ||||||
| 主題Scheme | NDC | |||||
| 主題 | 410 | |||||
| 学位名 | ||||||
| 学位名 | 博士(数理科学) | |||||
| 学位 | ||||||
| 値 | doctoral | |||||
| 学位分野 | ||||||
| Mathematical Sciences (数理科学) | ||||||
| 学位授与機関 | ||||||
| 学位授与機関名 | University of Tokyo (東京大学) | |||||
| 研究科・専攻 | ||||||
| Graduate School of Mathematical Sciences (数理科学研究科) | ||||||
| 学位授与年月日 | ||||||
| 学位授与年月日 | 2012-03-22 | |||||
| 学位授与番号 | ||||||
| 学位授与番号 | 甲第28380号 | |||||
| 学位記番号 | ||||||
| 博数理第388号 | ||||||
