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OverviewOver 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. Full Product DetailsAuthor: Ehud Hrushovski , François LoeserPublisher: Princeton University Press Imprint: Princeton University Press Volume: 223 Dimensions: Width: 17.80cm , Height: 1.50cm , Length: 25.40cm Weight: 0.397kg ISBN: 9780691161693ISBN 10: 0691161690 Pages: 232 Publication Date: 09 February 2016 Audience: College/higher education , Professional and scholarly , Tertiary & Higher Education , Professional & Vocational Format: Paperback Publisher's Status: Active Availability: Temporarily unavailable  The supplier advises that this item is temporarily unavailable. It will be ordered for you and placed on backorder. Once it does come back in stock, we will ship it out to you. Language: English Table of ContentsReviewsA major achievement, both in rigid algebraic geometry, and as an application of model-theoretic and stability-theoretic methods to algebraic geometry. --Anand Pillay, MathSciNet 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 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 """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" Author InformationEhud 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. Franois Loeser is professor of mathematics at Pierre-and-Marie-Curie University in Paris. Tab Content 6Author Website:Countries AvailableAll regions |
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