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On a Generalized Brauer Group in Mixed Characteristic Cases
http://hdl.handle.net/2261/0002005203
http://hdl.handle.net/2261/00020052030336c17a-4bb9-43c8-a16d-01c030c342b0
名前 / ファイル | ライセンス | アクション |
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jms270102.pdf (234.2 KB)
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Item type | 紀要論文 / Departmental Bulletin Paper(1) | |||||||
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公開日 | 2022-06-23 | |||||||
タイトル | ||||||||
タイトル | On a Generalized Brauer Group in Mixed Characteristic Cases | |||||||
言語 | en | |||||||
言語 | ||||||||
言語 | eng | |||||||
キーワード | ||||||||
主題 | Brauer group | |||||||
言語 | en | |||||||
主題Scheme | Other | |||||||
キーワード | ||||||||
主題 | Gersten's conjecture | |||||||
言語 | en | |||||||
主題Scheme | Other | |||||||
キーワード | ||||||||
主題 | local-global principle | |||||||
言語 | en | |||||||
主題Scheme | Other | |||||||
資源タイプ | ||||||||
資源 | http://purl.org/coar/resource_type/c_6501 | |||||||
タイプ | departmental bulletin paper | |||||||
著者 |
Sakagaito, Makoto
× Sakagaito, Makoto
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著者所属 | ||||||||
言語 | en | |||||||
著者所属 | Indian Institute of Science Education and Research, Mohali | |||||||
抄録 | ||||||||
内容記述タイプ | Abstract | |||||||
内容記述 | We define a generalization of the Brauer group $\HB^{n}(X)$ for an equi-dimensional scheme $X$ and $n>0$. In the case where $X$ is the spectrum of a local ring of a smooth algebra over a discrete valuation ring, $\HB^{n}(X)$ agrees with the \'{e}tale motivic cohomology $\HO^{n+1}_{\mathrm{\acute{e}t}}\left(X, \mathbb{Z}(n-1)\right)$. We prove (a part of) the Gersten-type conjecture for the generalized Brauer group for a local ring of a smooth algebra over a mixed characteristic discrete valuation ring and an isomorphism $\HB^{n}\left( R \right) \simeq \HB^{n}\left( k \right)$ for a henselian local ring $R$ of a smooth algebra over a mixed characteristic discrete valuation ring and the residue field $k$ of $R$. As an application, we show local-global principles for Galois cohomology groups over function fields of smooth curves over a mixed characteristic excellent henselian discrete valuation ring. | |||||||
言語 | en | |||||||
書誌情報 |
en : Journal of Mathematical Sciences The University of Tokyo 巻 27, 号 1, p. 29-64, 発行日 2020-11-06 |
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ISSN | ||||||||
収録物識別子タイプ | ISSN | |||||||
収録物識別子 | 13405705 | |||||||
書誌レコードID | ||||||||
収録物識別子タイプ | NCID | |||||||
収録物識別子 | AA11021653 | |||||||
Mathmatical Subject Classification | ||||||||
en | ||||||||
14F30(MSC2010) | ||||||||
Mathmatical Subject Classification | ||||||||
en | ||||||||
14F22(MSC2010) | ||||||||
出版者 | ||||||||
言語 | en | |||||||
出版者 | Graduate School of Mathematical Sciences, The University of Tokyo | |||||||
原稿受領日 | ||||||||
2019-06-05 |