<電子ブック>
Motivic Integration / by Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag
(Progress in Mathematics. ISSN:2296505X ; 325)
版 | 1st ed. 2018. |
---|---|
出版者 | (New York, NY : Springer New York : Imprint: Birkhäuser) |
出版年 | 2018 |
大きさ | XX, 526 p. 47 illus : online resource |
著者標目 | *Chambert-Loir, Antoine author Nicaise, Johannes author Sebag, Julien author SpringerLink (Online service) |
件 名 | LCSH:Algebraic geometry LCSH:K-theory FREE:Algebraic Geometry FREE:K-Theory |
一般注記 | Introduction -- Prologue: p-adic Integration -- Analytic Manifolds -- The Theorem of Batyrev-Kontsevich -- Igusa's Local Zeta Function -- The Grothendieck Ring of Varieties -- Additive Invariants on Algebraic Varieties -- Motivic Measures -- Cohomolical Realizations -- Localization, Completion, and Modification -- The Theorem of Bittner -- The Theorem of Larsen–Lunts and Its Applications -- Arc Schemes -- Weil Restriction -- Jet Schemes -- The Arc Scheme of a Variety -- Topological Properties of Arc Schemes -- The Theorem of Grinberg–Kazhdan–Drinfeld -- Greenberg Schemes -- Complete Discrete Valuation Rings -- The Ring Schemes Rn -- Greenberg Schemes -- Topological Properties of Greenberg Schemes -- Structure Theoremes for Greenberg Schemes -- Greenberg Approximation on Formal Schemes -- The Structure of the Truncation Morphisms -- Greenberg Schemes and Morphisms of Formal Schemes -- Motivic Integration -- Motivic Integration in the Smooth Case -- The Volume of a Constructibel Subset -- Measurable Subsets of Greenberg Schemes -- Motivic Integrals -- Semi-algebraic Subsets of Greenberg Schemes -- Applications -- Kapranov's Motivic Zeta Function -- Valuations and the Space of Arcs -- Motivic Volume and Birational Invariants -- Denef-Loeser's Zeta Function and the Monodromy Conjecture -- Motivic Invariants of Non-Archimedean Analytic Spaces -- Motivic Zeta Functions of Formal Shemes and Analytic Spaces -- Motivic Serre Invariants of Algebraic Varieties -- Appendix -- Constructibility in Algebraic Geometry -- Birational Geometry -- Formal and Non-Archimedean Geometry -- Index -- Bibliography This monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since. HTTP:URL=https://doi.org/10.1007/978-1-4939-7887-8 |
目次/あらすじ
所蔵情報を非表示
電子ブック | 配架場所 | 資料種別 | 巻 次 | 請求記号 | 状 態 | 予約 | コメント | ISBN | 刷 年 | 利用注記 | 指定図書 | 登録番号 |
---|---|---|---|---|---|---|---|---|---|---|---|---|
電子ブック | オンライン | 電子ブック |
|
Springer eBooks | 9781493978878 |
|
電子リソース |
|
EB00198082 |
類似資料
この資料の利用統計
このページへのアクセス回数:3回
※2017年9月4日以降