Coverart for item
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

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
Creator
Contributor
Author
Subject
Genre
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
Member of
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
Instantiates
Publication
Copyright
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
Publication
Copyright
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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