rdf-syntax-grammar
mods:
  schema location: http://www.loc.gov/mods/v3 http://www.loc.gov/standards/mods/v3/mods-3-2.xsd
  title info:
    title: Motivic Integration
  name:
    name part: Chambert-Loir, Antoine.
    role:
      role term: creator
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Nicaise, Johannes.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: Sebag, Julien.
    role:
      role term: author.
    role:
      role term: aut
    role:
      role term: http://id.loc.gov/vocabulary/relators/aut
  name:
    name part: SpringerLink (Online service)
  type of resource: text
  origin info:
    place:
      place term: xxu
    date issued: 2018
    edition: 1st ed. 2018.
    issuance: monographic
  language:
    language term: eng
  physical description:
    form: electronic
    form: electronic resource
    reformatting quality: access
    form: remote
    extent: XX, 526 p. 47 illus. online resource.
  abstract: 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. .
  table of contents: 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.
  note: by Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag.
  subject:
    topic: Algebraic geometry
  subject:
    topic: K-theory
  subject:
    topic: Algebraic Geometry
  subject:
    topic: K-Theory
  classification: QA564-609
  classification: 516.35
  related item:
    title info:
      title: Springer eBooks
  related item:
    title info:
      title: Progress in Mathematics, 325
  identifier: 9781493978878
  identifier: https://doi.org/10.1007/978-1-4939-7887-8
  record info:
    record creation date: 180914
    record change date: 20191024152609.0
    record identifier: 978-1-4939-7887-8