Non-Archimedean Tame Topology and Stably Dominated Types

AvEhud Hrushovski,François Loeser

Inbunden, Engelska, 2016

Del i serien Annals of Mathematics Studies

1 824 kr

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Häftad

1 037 kr

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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.

Produktinformation

Utgivningsdatum:2016-02-09
Mått:178 x 254 x 19 mm
Vikt:567 g
Format:Inbunden
Språk:Engelska
Serie:Annals of Mathematics Studies
Antal sidor:232
Förlag:Princeton University Press
ISBN:9780691161686

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

Ehud Hrushovski is professor of mathematics at the Hebrew University of Jerusalem. He is the coauthor of Finite Structures with Few Types (Princeton) and Stable Domination and Independence in Algebraically Closed Valued Fields. Francois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris.

Recensioner i media

"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNet

Innehållsförteckning

*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215

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Non-Archimedean Tame Topology and Stably Dominated Types

AvEhud Hrushovski,François Loeser

Inbunden, Engelska, 2016

Del i serien Annals of Mathematics Studies

1 824 kr

Beställningsvara. Skickas inom 5-8 vardagar. Fri frakt över 249 kr.

Fler format och utgåvor

Häftad

1 037 kr

Beskrivning

Produktinformation

Utgivningsdatum:2016-02-09
Mått:178 x 254 x 19 mm
Vikt:567 g
Format:Inbunden
Språk:Engelska
Serie:Annals of Mathematics Studies
Antal sidor:232
Förlag:Princeton University Press
ISBN:9780691161686

Utforska kategorier

Topologi inom Naturvetenskap och teknik
Matematik inom Naturvetenskap och teknik

Mer om författaren

Recensioner i media

"A major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry."---Anand Pillay, MathSciNet

Innehållsförteckning

*Frontmatter, pg. i*Contents, pg. v*1. Introduction, pg. 1*2. Preliminaries, pg. 8*3. The space v of stably dominated types, pg. 37*4. Definable compactness, pg. 57*5. A closer look at the stable completion, pg. 70*6. GAMMA-internal spaces, pg. 76*7. Curves, pg. 92*8. Strongly stably dominated points, pg. 104*9. Specializations and ACV2F, pg. 119*10. Continuity of homotopies, pg. 142*11. The main theorem, pg. 154*12. The smooth case, pg. 177*13. An equivalence of categories, pg. 183*14. Applications to the topology of Berkovich spaces, pg. 187*Bibliography, pg. 207*Index, pg. 211*List of notations, pg. 215