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

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

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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Superior document:Title is part of eBook package: De Gruyter EBOOK PACKAGE COMPLETE 2016
VerfasserIn:
Hrushovski, Ehud,
Loeser, François,
Place / Publishing House:Princeton, NJ : : Princeton University Press, , [2016]
©2016
Year of Publication:2016
Language:English
Series:Annals of Mathematics Studies ; 192
Online Access:
Physical Description:1 online resource (232 p.)
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100 1 |a Hrushovski, Ehud,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
245 1 0 |a Non-Archimedean Tame Topology and Stably Dominated Types (AM-192) /  |c François Loeser, Ehud Hrushovski. 
264 1 |a Princeton, NJ :   |b Princeton University Press,   |c [2016] 
264 4 |c ©2016 
300 |a 1 online resource (232 p.) 
336 |a text  |b txt  |2 rdacontent 
337 |a computer  |b c  |2 rdamedia 
338 |a online resource  |b cr  |2 rdacarrier 
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490 0 |a Annals of Mathematics Studies ;  |v 192 
505 0 0 |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 
506 0 |a restricted access  |u http://purl.org/coar/access_right/c_16ec  |f online access with authorization  |2 star 
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. 
530 |a Issued also in print. 
538 |a Mode of access: Internet via World Wide Web. 
546 |a In English. 
588 0 |a Description based on online resource; title from PDF title page (publisher's Web site, viewed 31. Jan 2022) 
650 0 |a Geometry, Algebraic. 
650 0 |a Tame algebras. 
650 0 |a Topology. 
650 7 |a MATHEMATICS / Geometry / Analytic.  |2 bisacsh 
653 |a Abhyankar property. 
653 |a Berkovich space. 
653 |a Galois orbit. 
653 |a Riemann-Roch. 
653 |a Zariski dense open set. 
653 |a Zariski open subset. 
653 |a Zariski topology. 
653 |a algebraic geometry. 
653 |a algebraic variety. 
653 |a algebraically closed valued field. 
653 |a analytic geometry. 
653 |a birational invariant. 
653 |a canonical extension. 
653 |a connectedness. 
653 |a continuity criteria. 
653 |a continuous definable map. 
653 |a continuous map. 
653 |a curve fibration. 
653 |a definable compactness. 
653 |a definable function. 
653 |a definable homotopy type. 
653 |a definable set. 
653 |a definable space. 
653 |a definable subset. 
653 |a definable topological space. 
653 |a definable topology. 
653 |a definable type. 
653 |a definably compact set. 
653 |a deformation retraction. 
653 |a finite simplicial complex. 
653 |a finite-dimensional vector space. 
653 |a forward-branching point. 
653 |a fundamental space. 
653 |a g-continuity. 
653 |a g-continuous. 
653 |a g-open set. 
653 |a germ. 
653 |a good metric. 
653 |a homotopy equivalence. 
653 |a homotopy. 
653 |a imaginary base set. 
653 |a ind-definable set. 
653 |a ind-definable subset. 
653 |a inflation homotopy. 
653 |a inflation. 
653 |a inverse limit. 
653 |a iso-definability. 
653 |a iso-definable set. 
653 |a iso-definable subset. 
653 |a iterated place. 
653 |a linear topology. 
653 |a main theorem. 
653 |a model theory. 
653 |a morphism. 
653 |a natural functor. 
653 |a non-archimedean geometry. 
653 |a non-archimedean tame topology. 
653 |a o-minimal formulation. 
653 |a o-minimality. 
653 |a orthogonality. 
653 |a path. 
653 |a pro-definable bijection. 
653 |a pro-definable map. 
653 |a pro-definable set. 
653 |a pro-definable subset. 
653 |a pseudo-Galois covering. 
653 |a real numbers. 
653 |a relatively compact set. 
653 |a residue field extension. 
653 |a retraction. 
653 |a schematic distance. 
653 |a semi-lattice. 
653 |a sequence. 
653 |a smooth case. 
653 |a smoothness. 
653 |a stability theory. 
653 |a stable completion. 
653 |a stable domination. 
653 |a stably dominated point. 
653 |a stably dominated type. 
653 |a stably dominated. 
653 |a strong stability. 
653 |a substructure. 
653 |a topological embedding. 
653 |a topological space. 
653 |a topological structure. 
653 |a topology. 
653 |a transcendence degree. 
653 |a v-continuity. 
653 |a valued field. 
653 |a Γ-internal set. 
653 |a Γ-internal space. 
653 |a Γ-internal subset. 
700 1 |a Loeser, François,   |e author.  |4 aut  |4 http://id.loc.gov/vocabulary/relators/aut 
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773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton Annals of Mathematics eBook-Package 1940-2020  |z 9783110494914  |o ZDB-23-PMB 
773 0 8 |i Title is part of eBook package:  |d De Gruyter  |t Princeton University Press Complete eBook-Package 2016  |z 9783110638592 
776 0 |c print  |z 9780691161693 
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