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 t...
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| Weitere Verfasser: | , , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Cambridge, UK ; New York, NY :
Cambridge University Press,
2011.
|
| Schriftenreihe: | London Mathematical Society lecture note series ;
383. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | "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"-- |
| Beschreibung: | 1 online resource (xi, 334 pages) : illustrations |
| Bibliographie: | Includes bibliographical references. |
| ISBN: | 9781139145022 1139145029 9780511667534 0511667531 1139141708 9781139141703 1283316617 9781283316613 9786613316615 661331661X 1139140825 9781139140829 1139137697 9781139137690 |
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| 588 | 0 | |a Print version record. | |
| 505 | 8 | |a 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. | |
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| contents | 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. |
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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"--</subfield><subfield code="c">Provided by publisher</subfield></datafield><datafield tag="588" ind1="0" ind2=" "><subfield code="a">Print version record.</subfield></datafield><datafield tag="505" ind1="8" ind2=" "><subfield code="a">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. 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| id | ZDB-4-EBA-ocn768111288 |
| illustrated | Illustrated |
| indexdate | 2024-11-27T13:18:08Z |
| institution | BVB |
| isbn | 9781139145022 1139145029 9780511667534 0511667531 1139141708 9781139141703 1283316617 9781283316613 9786613316615 661331661X 1139140825 9781139140829 1139137697 9781139137690 |
| language | English |
| oclc_num | 768111288 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (xi, 334 pages) : illustrations |
| psigel | ZDB-4-EBA |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | Cambridge University Press, |
| record_format | marc |
| 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. Volume 1 / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. Cambridge, UK ; New York, NY : Cambridge University Press, 2011. 1 online resource (xi, 334 pages) : illustrations text txt rdacontent computer c rdamedia online resource cr rdacarrier London Mathematical Society lecture note series ; 383 "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"-- Provided by publisher Print version record. 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. Includes bibliographical references. English. 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 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Géométrie algébrique. MATHEMATICS Logic. bisacsh MATHEMATICS Infinity. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory fast Valued fields fast Cluckers, Raf. Nicaise, Johannes. Sebag, Julien. Print version: Motivic integration and its interactions with model theory and non-Archimedean geometry. Volume 1. Cambridge, UK ; New York, NY : Cambridge University Press, 2011 9780521149761 (DLC) 2011021254 (OCoLC)707967565 London Mathematical Society lecture note series ; 383. http://id.loc.gov/authorities/names/n42015587 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=400559 Volltext |
| spellingShingle | Motivic integration and its interactions with model theory and non-Archimedean geometry. London Mathematical Society lecture note series ; 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. 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 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Géométrie algébrique. MATHEMATICS Logic. bisacsh MATHEMATICS Infinity. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory 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/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. Volume 1 / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
| title_fullStr | Motivic integration and its interactions with model theory and non-Archimedean geometry. Volume 1 / edited by Raf Cluckers, Johannes Nicaise, Julien Sebag. |
| title_full_unstemmed | Motivic integration and its interactions with model theory and non-Archimedean geometry. Volume 1 / 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 Geometry, Algebraic. http://id.loc.gov/authorities/subjects/sh85054140 Théorie des modèles. Corps valués. Espaces analytiques. Géométrie algébrique. MATHEMATICS Logic. bisacsh MATHEMATICS Infinity. bisacsh Analytic spaces fast Geometry, Algebraic fast Model theory fast Valued fields fast |
| topic_facet | Model theory. Valued fields. Analytic spaces. Geometry, Algebraic. Théorie des modèles. Corps valués. Espaces analytiques. Géométrie algébrique. MATHEMATICS Logic. MATHEMATICS Infinity. Analytic spaces Geometry, Algebraic Model theory Valued fields |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=400559 |
| work_keys_str_mv | AT cluckersraf motivicintegrationanditsinteractionswithmodeltheoryandnonarchimedeangeometryvolume1 AT nicaisejohannes motivicintegrationanditsinteractionswithmodeltheoryandnonarchimedeangeometryvolume1 AT sebagjulien motivicintegrationanditsinteractionswithmodeltheoryandnonarchimedeangeometryvolume1 |