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...
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| Hauptverfasser: | , |
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Princeton, NJ
Princeton University Press
[2016]
|
| Schriftenreihe: | Annals of mathematics studies
number 192 |
| Schlagworte: | |
| Online-Zugang: | FAW01 FHA01 FHR01 FKE01 FLA01 TUM01 UPA01 FAB01 FCO01 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-Ressource (x, 216 Seiten) |
| ISBN: | 9781400881222 9780691161686 9780691161693 |
| DOI: | 10.1515/9781400881222 |
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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 | ||
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| indexdate | 2024-07-10T07:30:39Z |
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| isbn | 9781400881222 9780691161686 9780691161693 |
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| spelling | Hrushovski, Ehud 1959- (DE-588)1103143778 aut Non-archimedean tame topology and stably dominated types Ehud Hrushovski, François Loeser Princeton, NJ Princeton University Press [2016] © 2016 1 Online-Ressource (x, 216 Seiten) txt rdacontent c rdamedia cr rdacarrier Annals of mathematics studies number 192 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 Tame algebras Loeser, François aut Erscheint auch als Druck-Ausgabe 978-0-691-16168-6 Annals of mathematics studies number 192 (DE-604)BV040389493 192 https://doi.org/10.1515/9781400881222 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Hrushovski, Ehud 1959- Loeser, François Non-archimedean tame topology and stably dominated types Annals of mathematics studies Tame algebras |
| title | Non-archimedean tame topology and stably dominated types |
| 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 |
| topic_facet | Tame algebras |
| url | https://doi.org/10.1515/9781400881222 |
| volume_link | (DE-604)BV040389493 |
| work_keys_str_mv | AT hrushovskiehud nonarchimedeantametopologyandstablydominatedtypes AT loeserfrancois nonarchimedeantametopologyandstablydominatedtypes |