| 书目名称 | The Brauer–Grothendieck Group |
| 编辑 | Jean-Louis Colliot-Thélène,Alexei N. Skorobogatov |
| 视频video | http://file.papertrans.cn/906/905416/905416.mp4 |
| 概述 | Provides a self-contained introduction to the Brauer group of schemes.Presents recent applications to rational points on varieties and to rationality problems in algebraic geometry.Offers a detailed g |
| 丛书名称 | Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge / A Series of Modern Surveys in Mathemati |
| 图书封面 |  |
| 描述 | This monograph provides a systematic treatment of the Brauer group of schemes, from the foundational work of Grothendieck to recent applications in arithmetic and algebraic geometry. .The importance of the cohomological Brauer group for applications to Diophantine equations and algebraic geometry was discovered soon after this group was introduced by Grothendieck. The Brauer–Manin obstruction plays a crucial role in the study of rational points on varieties over global fields. The birational invariance of the Brauer group was recently used in a novel way to establish the irrationality of many new classes of algebraic varieties. The book covers the vast theory underpinning these and other applications...Intended as an introduction to cohomological methods in algebraic geometry, most of the book is accessible to readers with a knowledge of algebra, algebraic geometry and algebraic number theory at graduate level. Much of the more advanced material is not readily available inbook form elsewhere; notably, de Jong’s proof of Gabber’s theorem, the specialisation method and applications of the Brauer group to rationality questions, an in-depth study of the Brauer–Manin obstruction, and pr |
| 出版日期 | Book 2021 |
| 关键词 | Brauer group; Scheme; Brauer-Manin obstruction; Abelian variety; K3 surface; Kuga-Satake construction; Tat |
| 版次 | 1 |
| doi | https://doi.org/10.1007/978-3-030-74248-5 |
| isbn_ebook | 978-3-030-74248-5Series ISSN 0071-1136 Series E-ISSN 2197-5655 |
| issn_series | 0071-1136 |
| copyright | The Editor(s) (if applicable) and The Author(s), under exclusive license to Springer Nature Switzerl |
|Archiver|手机版|小黑屋|
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