Motivic integration and its interactions with model theory and non-Archimedean geometry, Volume 1
The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the dif...
Gespeichert in:
- Weitere Titel:
- Motivic Integration & its Interactions with Model Theory & Non-Archimedean Geometry
- Hauptverfasser:
- , ,
- Format:
- Elektronisch E-Book
- Sprache:
- Englisch
- Veröffentlicht:
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2011
- Zusammenfassung:
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The development of Maxim Kontsevich's initial ideas on motivic integration has unexpectedly influenced many other areas of mathematics, ranging from the Langlands program over harmonic analysis, to non-Archimedean analysis, singularity theory and birational geometry. This book assembles the different theories of motivic integration and their applications for the first time, allowing readers to compare different approaches and assess their individual strengths. All of the necessary background is provided to make the book accessible to graduate students and researchers from algebraic geometry, model theory and number theory. Applications in several areas are included so that readers can see motivic integration at work in other domains. In a rapidly-evolving area of research this book will prove invaluable. This first volume contains introductory texts on the model theory of valued fields, different approaches to non-Archimedean geometry, and motivic integration on algebraic varieties and non-Archimedean spaces
- Umfang:
- 1 online resource (xi, 334 pages) digital, PDF file(s)
- Anmerkungen:
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Title from publisher's bibliographic system (viewed on 05 Oct 2015)
Machine generated contents note: 1. Introduction Raf Cluckers, Johannes Nicaise and Julien Sebag; 2. Introduction to the model theory of valued fields Zoe; Chatzidakis; 3. On the definition of rigid analytic spaces Siegfried Bosch; 4. Topological rings in rigid geometry Fumiharu Kato; 5. The Grothendieck ring of varieties Johannes Nicaise and Julien Sebag; 6. A short course on geometric motivic integration Manuel Blickle; 7. Motivic invariants of rigid varieties and applications to complex singularities Johannes Nicaise and Julien Sebag; 8. Motivic integration in mixed characteristic with bounded ramification: a summary Raf Cluckers and François Loeser
Introductory notes on the model theory of valued fields / Zoé Chatzidakis -- On the definition of rigid analytic spaces / Siegfried Bosch -- Topological rings in rigid geometry / Fumiharu Kato -- The Grothendieck ring of varieties / Johannes Nicaise and Julien Sebag -- A short course on geometric motivic integration / Manuel Blickle -- Motivic invariants of rigid varieties and applications to complex singularities / Johannes Nicaise and Julien Sebag -- Motivic integration in mixed characteristic with bounded ramification: a summary / Raf Cluckers and François Loeser - Schriftenreihe:
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London Mathematical Society lecture note series
- ISBN:
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9780511667534
9780521149761 - DOI:
- 10.1017/CBO9780511667534
- Schlagworte:
- Links:
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