View in EDS PDF Full Text ePub Full Text

Non-Archimedean Tame Topology and Stably Dominated Types

Saved in:
Bibliographic Details
Title: Non-Archimedean Tame Topology and Stably Dominated Types
Description: 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.
Authors: Ehud Hrushovski, François Loeser
Resource Type: eBook.
Subjects: Tame algebras
Categories: MATHEMATICS / Geometry / Analytic, MATHEMATICS / Geometry / Algebraic, MATHEMATICS / Topology
Database: eBook Collection (EBSCOhost)
FullText Links:
  – Type: ebook-pdf
  – Type: ebook-epub
Text:
  Availability: 0
Header DbId: nlebk
DbLabel: eBook Collection (EBSCOhost)
An: 1090926
RelevancyScore: 1070
AccessLevel: 6
PubType: eBook
PubTypeId: ebook
PreciseRelevancyScore: 1070.4580078125
IllustrationInfo
ImageInfo – Size: thumb
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$1090926$PDF&s=r
– Size: medium
  Target: https://rps2images.ebscohost.com/rpsweb/othumb?id=NL$1090926$PDF&s=d
Items – Name: Title
  Label: Title
  Group: Ti
  Data: Non-Archimedean Tame Topology and Stably Dominated Types
– Name: Abstract
  Label: Description
  Group: Ab
  Data: 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.
– Name: Author
  Label: Authors
  Group: Au
  Data: <searchLink fieldCode="AR" term="%22Ehud+Hrushovski%22">Ehud Hrushovski</searchLink><br /><searchLink fieldCode="AR" term="%22François+Loeser%22">François Loeser</searchLink>
– Name: TypePub
  Label: Resource Type
  Group: TypPub
  Data: eBook.
– Name: Subject
  Label: Subjects
  Group: Su
  Data: <searchLink fieldCode="DE" term="%22Tame+algebras%22">Tame algebras</searchLink>
– Name: SubjectBISAC
  Label: Categories
  Group: Su
  Data: <searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+Analytic%22">MATHEMATICS / Geometry / Analytic</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Geometry+%2F+Algebraic%22">MATHEMATICS / Geometry / Algebraic</searchLink><br /><searchLink fieldCode="ZK" term="%22MATHEMATICS+%2F+Topology%22">MATHEMATICS / Topology</searchLink>
PLink https://search.ebscohost.com/login.aspx?direct=true&site=eds-live&db=nlebk&AN=1090926
RecordInfo BibRecord:
  BibEntity:
    Classifications:
      – Code: 512.4
        Scheme: ddc
        Type: prePub
    Languages:
      – Code: eng
        Text: English
    Subjects:
      – SubjectFull: Tame algebras
        Type: general
    Titles:
      – TitleFull: Non-Archimedean Tame Topology and Stably Dominated Types
        Type: main
  BibRelationships:
    HasContributorRelationships:
      – PersonEntity:
          Name:
            NameFull: Ehud Hrushovski
      – PersonEntity:
          Name:
            NameFull: François Loeser
      – PersonEntity:
          Name:
            NameFull: Ehud Hrushovski
      – PersonEntity:
          Name:
            NameFull: François Loeser
    IsPartOfRelationships:
      – BibEntity:
          Dates:
            – D: 01
              M: 01
              Type: published
              Y: 2016
            – D: 09
              M: 02
              Type: profile
              Y: 2016
          Identifiers:
            – Type: isbn-print
              Value: 9780691161686
            – Type: isbn-print
              Value: 9780691161693
            – Type: isbn-electronic
              Value: 9781400881222
          Numbering:
            – Type: volume
              Value: 00192
          Titles:
            – TitleFull: Non-Archimedean Tame Topology and Stably Dominated Types
              Type: main
ResultId 1