Non-Archimedean Tame Topology and Stably Dominated Types (AM-192) - Ehud Hrushovski, François Loeser

Non-Archimedean Tame Topology and Stably Dominated Types (AM-192)

Buch | Softcover
232 Seiten
2016
Princeton University Press (Verlag)
978-0-691-16169-3 (ISBN)
87,25 inkl. MwSt
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-archimed
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.

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.

*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

Erscheinungsdatum
Reihe/Serie Annals of Mathematics Studies
Verlagsort New Jersey
Sprache englisch
Maße 178 x 254 mm
Gewicht 397 g
Themenwelt Mathematik / Informatik Mathematik Geometrie / Topologie
ISBN-10 0-691-16169-0 / 0691161690
ISBN-13 978-0-691-16169-3 / 9780691161693
Zustand Neuware
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