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010   $a1-4008-8122-6
024 7 $a10.1515/9781400881222
035   $a(CKB)3710000000537982
035   $a(EBL)4198288
035   $a(OCoLC)933388580
035   $a(MiAaPQ)EBC4198288
035   $a(StDuBDS)EDZ0001756478
035   $a(DE-B1597)467880
035   $a(OCoLC)979911327
035   $a(DE-B1597)9781400881222
035   $a(Au-PeEL)EBL4198288
035   $a(CaPaEBR)ebr11135512
035   $a(CaONFJC)MIL882376
035   $a(EXLCZ)993710000000537982
100   $a20160115h20162016  uy             0
101 0 $aeng
135   $aurnnu---|u||u
181   $2rdacontent
182   $2rdamedia
183   $2rdacarrier
200 10$aNon-archimedean tame topology and stably dominated types /$fEhud Hrushovski, Franc?ois Loeser
210  1$aPrinceton, New Jersey ;$aOxford, [England] :$cPrinceton University Press,$d2016.
210  4$dİ2016
215   $a1 online resource (227 p.)
225 1 $aAnnals of Mathematics Studies ;$vNumber 192
300   $aDescription based upon print version of record.
311 0 $a0-691-16169-0 
311 0 $a0-691-16168-2 
320   $aIncludes bibliographical references and index.
327   $tFront matter --$tContents --$t1. Introduction --$t2. Preliminaries --$t3. The space v? of stably dominated types --$t4. Definable compactness --$t5. A closer look at the stable completion --$t6. ?-internal spaces --$t7. Curves --$t8. Strongly stably dominated points --$t9. Specializations and ACV2F --$t10. Continuity of homotopies --$t11. The main theorem --$t12. The smooth case --$t13. An equivalence of categories --$t14. Applications to the topology of Berkovich spaces --$tBibliography --$tIndex --$tList of notations
330   $aOver the field of real numbers, analytic geometry has long been in deep interaction with algebraic geometry, bringing the latter subject many of its topological insights. In recent decades, model theory has joined this work through the theory of o-minimality, providing finiteness and uniformity statements and new structural tools. For non-archimedean fields, such as the p-adics, the Berkovich analytification provides a connected topology with many thoroughgoing analogies to the real topology on the set of complex points, and it has become an important tool in algebraic dynamics and many other areas of geometry. This book lays down model-theoretic foundations for non-archimedean geometry. The methods combine o-minimality and stability theory. Definable types play a central role, serving first to define the notion of a point and then properties such as definable compactness. Beyond the foundations, the main theorem constructs a deformation retraction from the full non-archimedean space of an algebraic variety to a rational polytope. This generalizes previous results of V. Berkovich, who used resolution of singularities methods. No previous knowledge of non-archimedean geometry is assumed. Model-theoretic prerequisites are reviewed in the first sections.
410  0$aAnnals of mathematics studies ;$vNumber 192.
606   $aTame algebras
610   $aAbhyankar property.
610   $aBerkovich space.
610   $aGalois orbit.
610   $aRiemann-Roch.
610   $aZariski dense open set.
610   $aZariski open subset.
610   $aZariski topology.
610   $aalgebraic geometry.
610   $aalgebraic variety.
610   $aalgebraically closed valued field.
610   $aanalytic geometry.
610   $abirational invariant.
610   $acanonical extension.
610   $aconnectedness.
610   $acontinuity criteria.
610   $acontinuous definable map.
610   $acontinuous map.
610   $acurve fibration.
610   $adefinable compactness.
610   $adefinable function.
610   $adefinable homotopy type.
610   $adefinable set.
610   $adefinable space.
610   $adefinable subset.
610   $adefinable topological space.
610   $adefinable topology.
610   $adefinable type.
610   $adefinably compact set.
610   $adeformation retraction.
610   $afinite simplicial complex.
610   $afinite-dimensional vector space.
610   $aforward-branching point.
610   $afundamental space.
610   $ag-continuity.
610   $ag-continuous.
610   $ag-open set.
610   $agerm.
610   $agood metric.
610   $ahomotopy equivalence.
610   $ahomotopy.
610   $aimaginary base set.
610   $aind-definable set.
610   $aind-definable subset.
610   $ainflation homotopy.
610   $ainflation.
610   $ainverse limit.
610   $aiso-definability.
610   $aiso-definable set.
610   $aiso-definable subset.
610   $aiterated place.
610   $alinear topology.
610   $amain theorem.
610   $amodel theory.
610   $amorphism.
610   $anatural functor.
610   $anon-archimedean geometry.
610   $anon-archimedean tame topology.
610   $ao-minimal formulation.
610   $ao-minimality.
610   $aorthogonality.
610   $apath.
610   $apro-definable bijection.
610   $apro-definable map.
610   $apro-definable set.
610   $apro-definable subset.
610   $apseudo-Galois covering.
610   $areal numbers.
610   $arelatively compact set.
610   $aresidue field extension.
610   $aretraction.
610   $aschematic distance.
610   $asemi-lattice.
610   $asequence.
610   $asmooth case.
610   $asmoothness.
610   $astability theory.
610   $astable completion.
610   $astable domination.
610   $astably dominated point.
610   $astably dominated type.
610   $astably dominated.
610   $astrong stability.
610   $asubstructure.
610   $atopological embedding.
610   $atopological space.
610   $atopological structure.
610   $atopology.
610   $atranscendence degree.
610   $av-continuity.
610   $avalued field.
610   $a?-internal set.
610   $a?-internal space.
610   $a?-internal subset.
615  0$aTame algebras.
676   $a512.4
686   $aSI 830$2rvk
700   $aHrushovski$b Ehud$0725941
702   $aLoeser$b Franc?ois
801  0$bMiAaPQ
801  1$bMiAaPQ
801  2$bMiAaPQ
906   $aBOOK
912   $a9910822032303321
996   $aNon-archimedean tame topology and stably dominated types$94046851
997   $aUNINA