LEADER 04420nam 22005055 450 001 9910300137003321 005 20200702052809.0 010 $a1-4939-7887-X 024 7 $a10.1007/978-1-4939-7887-8 035 $a(CKB)4100000006671791 035 $a(MiAaPQ)EBC5517008 035 $a(DE-He213)978-1-4939-7887-8 035 $a(PPN)230537979 035 $a(EXLCZ)994100000006671791 100 $a20180914d2018 u| 0 101 0 $aeng 135 $aurcnu|||||||| 181 $ctxt$2rdacontent 182 $cc$2rdamedia 183 $acr$2rdacarrier 200 10$aMotivic Integration /$fby Antoine Chambert-Loir, Johannes Nicaise, Julien Sebag 205 $a1st ed. 2018. 210 1$aNew York, NY :$cSpringer New York :$cImprint: Birkhäuser,$d2018. 215 $a1 online resource (540 pages) 225 1 $aProgress in Mathematics,$x0743-1643 ;$v325 311 $a1-4939-7885-3 327 $aIntroduction -- 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. 330 $aThis monograph focuses on the geometric theory of motivic integration, which takes its values in the Grothendieck ring of varieties. This theory is rooted in a groundbreaking idea of Kontsevich and was further developed by Denef & Loeser and Sebag. It is presented in the context of formal schemes over a discrete valuation ring, without any restriction on the residue characteristic. The text first discusses the main features of the Grothendieck ring of varieties, arc schemes, and Greenberg schemes. It then moves on to motivic integration and its applications to birational geometry and non-Archimedean geometry. Also included in the work is a prologue on p-adic analytic manifolds, which served as a model for motivic integration. With its extensive discussion of preliminaries and applications, this book is an ideal resource for graduate students of algebraic geometry and researchers of motivic integration. It will also serve as a motivation for more recent and sophisticated theories that have been developed since. . 410 0$aProgress in Mathematics,$x0743-1643 ;$v325 606 $aGeometry, Algebraic 606 $aK-theory 606 $aAlgebraic Geometry$3https://scigraph.springernature.com/ontologies/product-market-codes/M11019 606 $aK-Theory$3https://scigraph.springernature.com/ontologies/product-market-codes/M11086 615 0$aGeometry, Algebraic. 615 0$aK-theory. 615 14$aAlgebraic Geometry. 615 24$aK-Theory. 676 $a516.35 700 $aChambert-Loir$b Antoine$4aut$4http://id.loc.gov/vocabulary/relators/aut$0285206 702 $aNicaise$b Johannes$4aut$4http://id.loc.gov/vocabulary/relators/aut 702 $aSebag$b Julien$4aut$4http://id.loc.gov/vocabulary/relators/aut 906 $aBOOK 912 $a9910300137003321 996 $aMotivic Integration$92070203 997 $aUNINA