The Resource Non-archimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
Non-archimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
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The item Non-archimedean 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 Non-archimedean 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 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
- 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
- Non-archimedean tame topology and stably dominated types
- Title
- Non-archimedean 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 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
- 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
- Non-archimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 207-210) 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
- Non-archimedean tame topology and stably dominated types, Ehud Hrushovski, François Loeser
- Antecedent source
- unknown
- Bibliography note
- Includes bibliographical references (pages 207-210) 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 fa-external-link-square fa-fw"></i> Data from <span resource="http://link.sandiego.edu/portal/Non-archimedean-tame-topology-and-stably/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/Non-archimedean-tame-topology-and-stably/mKY8zXGRxcA/">Non-archimedean 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>
