Motivic integration and its interactions with model theory and non-Archimedean geometry /:
"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...
Saved in:
| Other Authors: | , , |
|---|---|
| Format: | Electronic eBook |
| Language: | English |
| Published: |
Cambridge, UK ; New York :
Cambridge University Press,
2011.
|
| Series: | London Mathematical Society lecture note series ;
383, 384. |
| Subjects: | |
| Online Access: | DE-862 DE-863 |
| 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. |
| Physical Description: | 1 online resource (2 volumes) : illustrations |
| Bibliography: | Includes bibliographical references. |
| ISBN: | 9781139145350 1139145355 9780521149761 0521149762 9781107648814 1107648815 9780511667534 0511667531 |
Staff View
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| 245 | 0 | 0 | |a Motivic integration and its interactions with model theory and non-Archimedean geometry / |c edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
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| 505 | 0 | |a 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. | |
| 520 | |a "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 | ||
| 520 | |a 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. | ||
| 504 | |a Includes bibliographical references. | ||
| 588 | 0 | |a Print version record. | |
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| 650 | 0 | |a Geometry, Algebraic. |0 http://id.loc.gov/authorities/subjects/sh85054140 | |
| 650 | 6 | |a Théorie des modèles. | |
| 650 | 6 | |a Corps valués. | |
| 650 | 6 | |a Espaces analytiques. | |
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| 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. |
| ctrlnum | (OCoLC)770036103 |
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| indexdate | 2025-04-11T08:37:31Z |
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| isbn | 9781139145350 1139145355 9780521149761 0521149762 9781107648814 1107648815 9780511667534 0511667531 |
| language | English |
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| series | London Mathematical Society lecture note series ; |
| series2 | London Mathematical Society lecture note series ; |
| spelling | Motivic integration and its interactions with model theory and non-Archimedean geometry / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. Cambridge, UK ; New York : Cambridge University Press, 2011. 1 online resource (2 volumes) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 383, 384 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. "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. Includes bibliographical references. Print version record. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Valued fields. http://id.loc.gov/authorities/subjects/sh85141938 Analytic spaces. http://id.loc.gov/authorities/subjects/sh85004789 Motives (Mathematics) http://id.loc.gov/authorities/subjects/sh93008066 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Motifs (Mathématiques) Géométrie algébrique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory fast Motives (Mathematics) fast Valued fields fast Cluckers, Raf. http://id.loc.gov/authorities/names/n2011034084 Nicaise, Johannes. http://id.loc.gov/authorities/names/n2011034085 Sebag, Julien. http://id.loc.gov/authorities/names/n2011034087 Print version: Motivic integration and its interactions with model theory and non-Archimedean geometry. Cambridge, UK ; New York : Cambridge University Press, 2011 9780521149761 (DLC) 2011021254 (OCoLC)760981625 London Mathematical Society lecture note series ; 383, 384. http://id.loc.gov/authorities/names/n42015587 |
| spellingShingle | Motivic integration and its interactions with model theory and non-Archimedean geometry / London Mathematical Society lecture note series ; 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. Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Valued fields. http://id.loc.gov/authorities/subjects/sh85141938 Analytic spaces. http://id.loc.gov/authorities/subjects/sh85004789 Motives (Mathematics) http://id.loc.gov/authorities/subjects/sh93008066 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Motifs (Mathématiques) Géométrie algébrique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory fast Motives (Mathematics) fast Valued fields fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh85086421 http://id.loc.gov/authorities/subjects/sh85141938 http://id.loc.gov/authorities/subjects/sh85004789 http://id.loc.gov/authorities/subjects/sh93008066 http://id.loc.gov/authorities/subjects/sh85054140 |
| title | Motivic integration and its interactions with model theory and non-Archimedean geometry / |
| title_auth | Motivic integration and its interactions with model theory and non-Archimedean geometry / |
| title_exact_search | Motivic integration and its interactions with model theory and non-Archimedean geometry / |
| title_full | Motivic integration and its interactions with model theory and non-Archimedean geometry / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
| title_fullStr | Motivic integration and its interactions with model theory and non-Archimedean geometry / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
| title_full_unstemmed | Motivic integration and its interactions with model theory and non-Archimedean geometry / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
| title_short | Motivic integration and its interactions with model theory and non-Archimedean geometry / |
| title_sort | motivic integration and its interactions with model theory and non archimedean geometry |
| topic | Model theory. http://id.loc.gov/authorities/subjects/sh85086421 Valued fields. http://id.loc.gov/authorities/subjects/sh85141938 Analytic spaces. http://id.loc.gov/authorities/subjects/sh85004789 Motives (Mathematics) http://id.loc.gov/authorities/subjects/sh93008066 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Motifs (Mathématiques) Géométrie algébrique. MATHEMATICS Infinity. bisacsh MATHEMATICS Logic. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory fast Motives (Mathematics) fast Valued fields fast |
| topic_facet | Model theory. Valued fields. Analytic spaces. Motives (Mathematics) Geometry, Algebraic. Théorie des modèles. Corps valués. Espaces analytiques. Motifs (Mathématiques) Géométrie algébrique. MATHEMATICS Infinity. MATHEMATICS Logic. Analytic spaces Geometry, Algebraic Model theory Valued fields |
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