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Non-archimedean tame topology and stably dominated types / / Ehud Hrushovski, François Loeser



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Autore: Hrushovski Ehud Visualizza persona
Titolo: Non-archimedean tame topology and stably dominated types / / Ehud Hrushovski, François Loeser Visualizza cluster
Pubblicazione: Princeton, New Jersey ; ; Oxford, [England] : , : Princeton University Press, , 2016
©2016
Descrizione fisica: 1 online resource (227 p.)
Disciplina: 512.4
Soggetto topico: Tame algebras
Soggetto non controllato: Abhyankar property
Berkovich space
Galois orbit
Riemann-Roch
Zariski dense open set
Zariski open subset
Zariski topology
algebraic geometry
algebraic variety
algebraically closed valued field
analytic geometry
birational invariant
canonical extension
connectedness
continuity criteria
continuous definable map
continuous map
curve fibration
definable compactness
definable function
definable homotopy type
definable set
definable space
definable subset
definable topological space
definable topology
definable type
definably compact set
deformation retraction
finite simplicial complex
finite-dimensional vector space
forward-branching point
fundamental space
g-continuity
g-continuous
g-open set
germ
good metric
homotopy equivalence
homotopy
imaginary base set
ind-definable set
ind-definable subset
inflation homotopy
inflation
inverse limit
iso-definability
iso-definable set
iso-definable subset
iterated place
linear topology
main theorem
model theory
morphism
natural functor
non-archimedean geometry
non-archimedean tame topology
o-minimal formulation
o-minimality
orthogonality
path
pro-definable bijection
pro-definable map
pro-definable set
pro-definable subset
pseudo-Galois covering
real numbers
relatively compact set
residue field extension
retraction
schematic distance
semi-lattice
sequence
smooth case
smoothness
stability theory
stable completion
stable domination
stably dominated point
stably dominated type
stably dominated
strong stability
substructure
topological embedding
topological space
topological structure
topology
transcendence degree
v-continuity
valued field
Γ-internal set
Γ-internal space
Γ-internal subset
Classificazione: SI 830
Persona (resp. second.): LoeserFrançois
Note generali: Description based upon print version of record.
Nota di bibliografia: Includes bibliographical references and index.
Nota di contenuto: Front matter -- Contents -- 1. Introduction -- 2. Preliminaries -- 3. The space v̂ of stably dominated types -- 4. Definable compactness -- 5. A closer look at the stable completion -- 6. Γ-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
Sommario/riassunto: 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.
Titolo autorizzato: Non-archimedean tame topology and stably dominated types  Visualizza cluster
ISBN: 1-4008-8122-6
Formato: Materiale a stampa
Livello bibliografico Monografia
Lingua di pubblicazione: Inglese
Record Nr.: 9910797708403321
Lo trovi qui: Univ. Federico II
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Serie: Annals of mathematics studies ; ; Number 192.