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  • Open Daily: 10am - 10pm
    Alley-side Pickup: 10am - 7pm

    3038 Hennepin Ave Minneapolis, MN
    612-822-4611

Open Daily: 10am - 10pm | Alley-side Pickup: 10am - 7pm
3038 Hennepin Ave Minneapolis, MN
612-822-4611
Motivic Integration

Motivic Integration

Chambert-Loir, Antoine
Nicaise, Johannes
Sebag, Julien

Hardcover

Series: Progress in Mathematics, Book 325

AlgebraGeometry

ISBN10: 1493978853
ISBN13: 9781493978854
Publisher: Birkhauser
Published: Sep 15 2018
Pages: 526
Weight: 2.07
Height: 1.19 Width: 6.14 Depth: 9.21
Language: English
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.

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