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Motivic Integration(Progress in Mathematics Vol. 325) hardcover XX, 526 p. 18

Chambert-Loir, Antoine, Nicaise, Johannes, Sebag, Julien 　著

在庫状況海外在庫有り	お届け予定日 1ヶ月
価格 \25,641（税込）

発行年月	2018年09月
出版社／提供元	Birkhauser Verlag AG
出版国	アメリカ合衆国
言語	英語
媒体	冊子
装丁	hardcover
ページ数／巻数	XX, 526 p. 47 illus.
ジャンル	洋書／理工学／数学／代数学
ISBN	9781493978854
商品コード	1027224460
本の性格	学術書
新刊案内掲載月	2018年11月
商品URL	https://kw.maruzen.co.jp/ims/itemDetail.html?itmCd=1027224460

内容

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.

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.