| Description |
1 online resource (2 volumes) : illustrations |
| Series |
London Mathematical Society lecture note series ; 383, 384 |
|
London Mathematical Society lecture note series ; 383, 384.
|
| Contents |
v. 1. Introduction ; 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 -- v. 2. Heights and measures on analytic spaces : a survey of recent results and some remarks / Antoine Chambert-Loir ; C-minimal structures without density assumption / Franc̜oise Delon ; Trees of definable sets in Zp / Immanuel Halupczok ; Triangulated motives over noetherian separated schemes / Florian Ivorra ; A survey of algebraic exzponential sums and some applications / Emmanuel Kowalski ; A motivic version of p-adic integration / Karl Rökaeus ; Absolute desingularization in characteristic zero / Michael Temkin |
| Summary |
"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 [work] 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 [work] will prove invaluable"--Page 4 of cover |
|
The 1st 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. The 2nd volume discusses various applications of non-Archimedian geometry, model theory and motivic integration and the interactions between these domains |
| Bibliography |
Includes bibliographical references |
| Notes |
Print version record |
| Subject |
Model theory.
|
|
Valued fields.
|
|
Analytic spaces.
|
|
Motives (Mathematics)
|
|
Geometry, Algebraic.
|
|
MATHEMATICS -- Infinity.
|
|
MATHEMATICS -- Logic.
|
|
Analytic spaces
|
|
Geometry, Algebraic
|
|
Model theory
|
|
Motives (Mathematics)
|
|
Valued fields
|
| Form |
Electronic book
|
| Author |
Cluckers, Raf.
|
|
Nicaise, Johannes.
|
|
Sebag, Julien.
|
| ISBN |
9781139145350 |
|
1139145355 |
|
9780521149761 |
|
0521149762 |
|
9781107648814 |
|
1107648815 |
|
9780511667534 |
|
0511667531 |
|
