Foundations of Rigid Geometry I

Material type: 図書

Author: 加藤, 文元ほか

Publisher: European Mathematical Society Publishing House

Publication date: 2018-01

Material Format: Paper

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Note (General)：: 出版タイプ： NARigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic g...

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Paper

Material Type: 図書
Title: Foundations of Rigid Geometry I
Author/Editor: 加藤, 文元
Kato, Fumiharu
藤原, 一宏
Fujijwara, Kazuhiro
Author Heading: 加藤, 文元
Kato, Fumiharu
藤原, 一宏
Fujijwara, Kazuhiro
Publication, Distribution, etc.: European Mathematical Society Publishing House
Publication Date: 2018-01
Publication Date (W3CDTF): 2018
Periodical title: EMS Monographs in Mathematics
Subject Heading: Rigid geometry, formal geometry, birational geometry
Target Audience: 一般
Note (General): 出版タイプ： NA
Rigid geometry is one of the modern branches of algebraic and arithmetic geometry. It has its historical origin in J. Tate’s rigid analytic geometry, which aimed at developing an analytic geometry over non-archimedean valued fields. Nowadays, rigid geometry is a discipline in its own right and has acquired vast and rich structures, based on discoveries of its relationship with birational and formal geometries.In this research monograph, foundational aspects of rigid geometry are discussed, putting emphasis on birational and topological features of rigid spaces. Besides the rigid geometry itself, topics include the general theory of formal schemes and formal algebraic spaces, based on a theory of complete rings which are not necessarily Noetherian. Also included is a discussion on the relationship with Tate‘s original rigid analytic geometry, V.G. Berkovich‘s analytic geometry and R. Huber‘s adic spaces. As a model example of applications, a proof of Nagata‘s compactification theorem for schemes is given in the appendix. The book is encyclopedic and almost self-contained.
identifier:oai:t2r2.star.titech.ac.jp:50402684
Related Material (DOI): 10.4171/135
https://doi.org/10.4171/135
Data Provider (Database): 国立情報学研究所 : 学術機関リポジトリデータベース（IRDB）（機関リポジトリ）
https://irdb.nii.ac.jp
Original Data Provider (Database): 東京科学大学 : 東京科学大学リサーチリポジトリ(T2R2)