The Resource Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
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The item Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.This item is available to borrow from 1 library branch.
Resource Information
The item Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of San Diego Libraries.
This item is available to borrow from 1 library branch.
 Summary
 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 ominimality, providing finiteness and uniformity statements and new structural tools. For nonarchimedean fields, such as the padics, 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 modeltheoretic foundations for nonarchimedean geometry. The methods combine ominimality 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 nonarchimedean 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 nonarchimedean geometry is assumed. Modeltheoretic prerequisites are reviewed in the first sections
 Language
 eng
 Extent
 1 online resource (vii, 216 pages)
 Contents

 6. [Gamma]internal spaces
 7. Curves
 8. Strongly stably dominated points
 9. Specializations and ACV2F
 10. Continuity of homotopies
 11. The main theorem
 12. The smooth case
 13. An equivalence of categories
 14. Applications to the topology of Berkovich spaces
 Bibliography
 Index
 List of notations
 Frontmatter
 Contents
 1. Introduction
 2. Preliminaries
 3. The space ̂v of stably dominated types
 4. Definable compactness
 5. A closer look at the stable completion
 Isbn
 9781400881222
 Label
 Nonarchimedean tame topology and stably dominated types
 Title
 Nonarchimedean tame topology and stably dominated types
 Statement of responsibility
 Ehud Hrushovski, François Loeser
 Language
 eng
 Summary
 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 ominimality, providing finiteness and uniformity statements and new structural tools. For nonarchimedean fields, such as the padics, 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 modeltheoretic foundations for nonarchimedean geometry. The methods combine ominimality 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 nonarchimedean 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 nonarchimedean geometry is assumed. Modeltheoretic prerequisites are reviewed in the first sections
 Cataloging source
 N$T
 http://library.link/vocab/creatorDate
 1959
 http://library.link/vocab/creatorName
 Hrushovski, Ehud
 Index
 index present
 Language note
 In English
 Literary form
 non fiction
 Nature of contents

 dictionaries
 bibliography
 http://library.link/vocab/relatedWorkOrContributorName
 Loeser, François
 Series statement
 Annals of mathematics studies
 Series volume
 number 192
 http://library.link/vocab/subjectName

 Tame algebras
 MATHEMATICS
 MATHEMATICS
 Tame algebras
 Label
 Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 207210) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 6. [Gamma]internal spaces
 7. Curves
 8. Strongly stably dominated points
 9. Specializations and ACV2F
 10. Continuity of homotopies
 11. The main theorem
 12. The smooth case
 13. An equivalence of categories
 14. Applications to the topology of Berkovich spaces
 Bibliography
 Index
 List of notations
 Frontmatter
 Contents
 1. Introduction
 2. Preliminaries
 3. The space ̂v of stably dominated types
 4. Definable compactness
 5. A closer look at the stable completion
 Control code
 ocn933388580
 Dimensions
 unknown
 Extent
 1 online resource (vii, 216 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781400881222
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 JSTOR
 Other control number
 10.1515/9781400881222
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctt193cj76
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)933388580
 Label
 Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
 Antecedent source
 unknown
 Bibliography note
 Includes bibliographical references (pages 207210) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Carrier MARC source
 rdacarrier
 Color
 multicolored
 Content category
 text
 Content type code

 txt
 Content type MARC source
 rdacontent
 Contents

 6. [Gamma]internal spaces
 7. Curves
 8. Strongly stably dominated points
 9. Specializations and ACV2F
 10. Continuity of homotopies
 11. The main theorem
 12. The smooth case
 13. An equivalence of categories
 14. Applications to the topology of Berkovich spaces
 Bibliography
 Index
 List of notations
 Frontmatter
 Contents
 1. Introduction
 2. Preliminaries
 3. The space ̂v of stably dominated types
 4. Definable compactness
 5. A closer look at the stable completion
 Control code
 ocn933388580
 Dimensions
 unknown
 Extent
 1 online resource (vii, 216 pages)
 File format
 unknown
 Form of item
 online
 Isbn
 9781400881222
 Level of compression
 unknown
 Media category
 computer
 Media MARC source
 rdamedia
 Media type code

 c
 Note
 JSTOR
 Other control number
 10.1515/9781400881222
 http://library.link/vocab/ext/overdrive/overdriveId
 22573/ctt193cj76
 Quality assurance targets
 not applicable
 Reformatting quality
 unknown
 Sound
 unknown sound
 Specific material designation
 remote
 System control number
 (OCoLC)933388580
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.sandiego.edu/portal/Nonarchimedeantametopologyandstably/mKY8zXGRxcA/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.sandiego.edu/portal/Nonarchimedeantametopologyandstably/mKY8zXGRxcA/">Nonarchimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.sandiego.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.sandiego.edu/">University of San Diego Libraries</a></span></span></span></span></div>