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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...
| Clasificación: | Libro Electrónico |
|---|---|
| Autores principales: | , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Princeton :
Princeton University Press,
2016.
|
| Colección: | Annals of mathematics studies ;
no. 192. |
| Temas: | |
| Acceso en línea: | Texto completo |
MARC
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| 100 | 1 | |a Hrushovski, Ehud, |d 1959- |e author. | |
| 245 | 1 | 0 | |a Non-archimedean tame topology and stably dominated types / |c Ehud Hrushovski, François Loeser. |
| 264 | 1 | |a Princeton : |b Princeton University Press, |c 2016. | |
| 264 | 4 | |c ©2016 | |
| 300 | |a 1 online resource (vii, 216 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
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| 490 | 1 | |a Annals of mathematics studies ; |v number 192 | |
| 504 | |a Includes bibliographical references (pages 207-210) and index. | ||
| 588 | 0 | |a Vendor-supplied metadata. | |
| 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. |
| 590 | |a JSTOR |b Books at JSTOR All Purchased | ||
| 590 | |a JSTOR |b Books at JSTOR Evidence Based Acquisitions | ||
| 590 | |a JSTOR |b Books at JSTOR Demand Driven Acquisitions (DDA) | ||
| 650 | 0 | |a Tame algebras. | |
| 650 | 6 | |a Algèbres régulières. | |
| 650 | 7 | |a MATHEMATICS |x Algebra |x Intermediate. |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS |x Topology. |2 bisacsh | |
| 650 | 7 | |a Tame algebras |2 fast | |
| 700 | 1 | |a Loeser, François, |e author. | |
| 776 | 0 | 8 | |i Print version: |z 9780691161686 |
| 830 | 0 | |a Annals of mathematics studies ; |v no. 192. | |
| 856 | 4 | 0 | |u https://jstor.uam.elogim.com/stable/10.2307/j.ctt18z4hkq |z Texto completo |
| 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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