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Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces
https://doi.org/10.15083/00005644
https://doi.org/10.15083/000056440444f964-37a8-4c50-ab92-99407417dfad
| 名前 / ファイル | ライセンス | アクション |
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UematsuT_25_3_PhD_a.pdf (2.7 MB)
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UematsuT_25_3_PhD_b.pdf (170.5 kB)
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| Item type | 学位論文 / Thesis or Dissertation(1) | |||||
|---|---|---|---|---|---|---|
| 公開日 | 2014-07-15 | |||||
| タイトル | ||||||
| タイトル | Uniform Representability of the Brauer Group of Diagonal Cubic Surfaces | |||||
| 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 | 10.15083/00005644 | |||||
| ID登録タイプ | JaLC | |||||
| その他のタイトル | ||||||
| その他のタイトル | 対角的3次曲面のBrauer群の統一的な表示可能性について | |||||
| 著者 |
Uematsu, Tetsuya
× Uematsu, Tetsuya |
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| 著者別名 | ||||||
| 識別子Scheme | WEKO | |||||
| 識別子 | 11757 | |||||
| 姓名 | 植松, 哲也 | |||||
| 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 | The Brauer group of a scheme is an effective tool for studying its arithmetic and geometric properties. For such purposes, we need to know not only the structure of the Brauer group as an abelian group, but also explicit generators such as those represented by norm residue symbols. Yu. I. Manin first studied such problems for diagonal cubic surfaces. He determined the structure of the Brauer group of some diagonal cubic surfaces and found its symbolic generators. In this dissertation, we generalize his result. We introduce the notion of uniformity for generators and prove the following two results: first, diagonal cubic surfaces of a particular form have such uniform generators represented by a norm residue symbol; secondly, in general, diagonal cubic surfaces have no uniform generator. The latter result states that there is a limit to extend the Manin's result stated above. | |||||
| 書誌情報 | 発行日 2013-03-25 | |||||
| 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 | 2013-03-25 | |||||
