Non-archimedean tame topology and stably dominated types /:
Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity stat...
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton :
Princeton University Press,
2016.
|
| Schriftenreihe: | Annals of mathematics studies ;
no. 192. |
| Schlagworte: | |
| Online-Zugang: | Volltext |
| Zusammenfassung: | Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections. |
| Beschreibung: | 1 online resource (vii, 216 pages) |
| Bibliographie: | Includes bibliographical references (pages 207-210) and index. |
| ISBN: | 9781400881222 1400881226 0691161682 9780691161686 0691161690 9780691161693 |
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| 520 | |a Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections. | ||
| 546 | |a In English. | ||
| 505 | 0 | 0 | |6 880-01 |t Frontmatter -- |t Contents -- |t 1. Introduction -- |t 2. Preliminaries -- |t 3. The space v̂ of stably dominated types -- |t 4. Definable compactness -- |t 5. A closer look at the stable completion -- |t 6. [Gamma]-internal spaces -- |t 7. Curves -- |t 8. Strongly stably dominated points -- |t 9. Specializations and ACV2F -- |t 10. Continuity of homotopies -- |t 11. The main theorem -- |t 12. The smooth case -- |t 13. An equivalence of categories -- |t 14. Applications to the topology of Berkovich spaces -- |t Bibliography -- |t Index -- |t List of notations. |
| 650 | 0 | |a Tame algebras. |0 http://id.loc.gov/authorities/subjects/sh86005677 | |
| 650 | 6 | |a Algèbres régulières. | |
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| 880 | 0 | 0 | |6 505-01/(S |t Frontmatter -- |t Contents -- |t 1. Introduction -- |t 2. Preliminaries -- |t 3. The space v̂ of stably dominated types -- |t 4. Definable compactness -- |t 5. A closer look at the stable completion -- |t 6. Γ-internal spaces -- |t 7. Curves -- |t 8. Strongly stably dominated points -- |t 9. Specializations and ACV2F -- |t 10. Continuity of homotopies -- |t 11. The main theorem -- |t 12. The smooth case -- |t 13. An equivalence of categories -- |t 14. Applications to the topology of Berkovich spaces -- |t Bibliography -- |t Index -- |t List of notations. |
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| author | Hrushovski, Ehud, 1959- Loeser, François |
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| contents | Frontmatter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. [Gamma]-internal spaces -- 7. Curves -- 8. Strongly stably dominated points -- 9. Specializations and ACV2F -- 10. Continuity of homotopies -- 11. The main theorem -- 12. The smooth case -- 13. An equivalence of categories -- 14. Applications to the topology of Berkovich spaces -- Bibliography -- Index -- List of notations. |
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| id | ZDB-4-EBA-ocn933388580 |
| illustrated | Not Illustrated |
| indexdate | 2024-11-27T13:26:57Z |
| institution | BVB |
| isbn | 9781400881222 1400881226 0691161682 9780691161686 0691161690 9780691161693 |
| language | English |
| oclc_num | 933388580 |
| open_access_boolean | |
| owner | MAIN DE-863 DE-BY-FWS |
| owner_facet | MAIN DE-863 DE-BY-FWS |
| physical | 1 online resource (vii, 216 pages) |
| psigel | ZDB-4-EBA |
| publishDate | 2016 |
| publishDateSearch | 2016 |
| publishDateSort | 2016 |
| publisher | Princeton University Press, |
| record_format | marc |
| series | Annals of mathematics studies ; |
| series2 | Annals of mathematics studies ; |
| spelling | Hrushovski, Ehud, 1959- author. https://id.oclc.org/worldcat/entity/E39PBJvCPykRCfpXQfXVH9rQbd http://id.loc.gov/authorities/names/n2002014399 Non-archimedean tame topology and stably dominated types / Ehud Hrushovski, François Loeser. Princeton : Princeton University Press, 2016. ©2016 1 online resource (vii, 216 pages) text txt rdacontent computer c rdamedia online resource cr rdacarrier text file PDF rda Annals of mathematics studies ; number 192 Includes bibliographical references (pages 207-210) and index. Vendor-supplied metadata. Over the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections. In English. 880-01 Frontmatter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. [Gamma]-internal spaces -- 7. Curves -- 8. Strongly stably dominated points -- 9. Specializations and ACV2F -- 10. Continuity of homotopies -- 11. The main theorem -- 12. The smooth case -- 13. An equivalence of categories -- 14. Applications to the topology of Berkovich spaces -- Bibliography -- Index -- List of notations. Tame algebras. http://id.loc.gov/authorities/subjects/sh86005677 Algèbres régulières. MATHEMATICS Algebra Intermediate. bisacsh MATHEMATICS Topology. bisacsh Tame algebras fast Loeser, François, author. http://id.loc.gov/authorities/names/no98065663 Print version: 9780691161686 Annals of mathematics studies ; no. 192. http://id.loc.gov/authorities/names/n42002129 FWS01 ZDB-4-EBA FWS_PDA_EBA https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1090926 Volltext 505-01/(S Frontmatter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. Γ-internal spaces -- 7. Curves -- 8. Strongly stably dominated points -- 9. Specializations and ACV2F -- 10. Continuity of homotopies -- 11. The main theorem -- 12. The smooth case -- 13. An equivalence of categories -- 14. Applications to the topology of Berkovich spaces -- Bibliography -- Index -- List of notations. |
| spellingShingle | Hrushovski, Ehud, 1959- Loeser, François Non-archimedean tame topology and stably dominated types / Annals of mathematics studies ; Frontmatter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. [Gamma]-internal spaces -- 7. Curves -- 8. Strongly stably dominated points -- 9. Specializations and ACV2F -- 10. Continuity of homotopies -- 11. The main theorem -- 12. The smooth case -- 13. An equivalence of categories -- 14. Applications to the topology of Berkovich spaces -- Bibliography -- Index -- List of notations. Tame algebras. http://id.loc.gov/authorities/subjects/sh86005677 Algèbres régulières. MATHEMATICS Algebra Intermediate. bisacsh MATHEMATICS Topology. bisacsh Tame algebras fast |
| subject_GND | http://id.loc.gov/authorities/subjects/sh86005677 |
| title | Non-archimedean tame topology and stably dominated types / |
| title_alt | Frontmatter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. [Gamma]-internal spaces -- 7. Curves -- 8. Strongly stably dominated points -- 9. Specializations and ACV2F -- 10. Continuity of homotopies -- 11. The main theorem -- 12. The smooth case -- 13. An equivalence of categories -- 14. Applications to the topology of Berkovich spaces -- Bibliography -- Index -- List of notations. |
| title_auth | Non-archimedean tame topology and stably dominated types / |
| title_exact_search | Non-archimedean tame topology and stably dominated types / |
| title_full | Non-archimedean tame topology and stably dominated types / Ehud Hrushovski, François Loeser. |
| title_fullStr | Non-archimedean tame topology and stably dominated types / Ehud Hrushovski, François Loeser. |
| title_full_unstemmed | Non-archimedean tame topology and stably dominated types / Ehud Hrushovski, François Loeser. |
| title_short | Non-archimedean tame topology and stably dominated types / |
| title_sort | non archimedean tame topology and stably dominated types |
| topic | Tame algebras. http://id.loc.gov/authorities/subjects/sh86005677 Algèbres régulières. MATHEMATICS Algebra Intermediate. bisacsh MATHEMATICS Topology. bisacsh Tame algebras fast |
| topic_facet | Tame algebras. Algèbres régulières. MATHEMATICS Algebra Intermediate. MATHEMATICS Topology. Tame algebras |
| url | https://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&AN=1090926 |
| work_keys_str_mv | AT hrushovskiehud nonarchimedeantametopologyandstablydominatedtypes AT loeserfrancois nonarchimedeantametopologyandstablydominatedtypes |