(Ebook) Non archimedean tame topology and stably dominated types 1st Edition by Ehud Hrushovski, François Loeser ISBN 9780691161686 0691161682

(Ebook) Non archimedean tame topology and stably dominated types 1st Edition by Ehud Hrushovski, François Loeser ISBN 9780691161686 0691161682

(Ebook) Non archimedean tame topology and stably dominated types 1st Edition by Ehud Hrushovski, François Loeser - Ebook PDF Instant Download/Delivery: 9780691161686 ,0691161682
Full download (Ebook) Non archimedean tame topology and stably dominated types 1st Edition after payment

Product details:

ISBN 10: 0691161682
ISBN 13: 9780691161686
Author: Ehud Hrushovski, François Loeser

(Ebook) Non archimedean tame topology and stably dominated types 1st Edition Table of contents:

1 Introduction

2 Preliminaries

2.1 Definable sets

2.2 Pro-definable and ind-definable sets

2.3 Definable types

2.4 Stable embeddedness

2.5 Orthogonality to a definable set

2.6 Stable domination

2.7 Review of ACVF

2.8 Γ-internal sets

2.9 Orthogonality to Γ

2.10 V̂ for stable definable V

2.11 Decomposition of definable types

2.12 Pseudo-Galois coverings

3 The space V̂ of stably dominated types

3.1 V̂ as a pro-definable set

3.2 Some examples

3.3 The notion of a definable topological space

3.4 V̂ as a topological space

3.5 The affine case

3.6 Simple points

3.7 v-open and g-open subsets, v+g-continuity

3.8 Canonical extensions

3.9 Paths and homotopies

3.10 Good metrics

3.11 Zariski topology

3.12 Schematic distance

4 Definable compactness

4.1 Definition of definable compactness

4.2 Characterization of definable compactness

5 A closer look at the stable completion

5.1 Âⁿ and spaces of semi-lattices

5.2 A representation of P̂ⁿ

5.3 Relative compactness

6 Γ-internal spaces

6.1 Preliminary remarks

6.2 Topological structure of Γ-internal subsets

6.3 Guessing definable maps by regular algebraic maps

6.4 Relatively Γ-internal subsets

7 Curves

7.1 Definability of Ĉ for a curve C

7.2 Definable types on curves

7.3 Lifting paths

7.4 Branching points

7.5 Construction of a deformation retraction

8 Strongly stably dominated points

8.1 Strongly stably dominated points

8.2 A Bertini theorem

8.3 Γ-internal sets and strongly stably dominated points

8.4 Topological properties of V#

9 Specializations and ACV²F

9.1 g-topology and specialization

9.2 v-topology and specialization

9.3 ACV²F

9.4 The map

9.5 Relative versions

9.6 g-continuity criterion

9.7 Some applications of the continuity criteria

9.8 The v-criterion on V̂

9.9 Definability of v- and g-criteria

10 Continuity of homotopies

10.1 Preliminaries

10.2 Continuity on relative ℙ¹

10.3 The inflation homotopy

10.4 Connectedness and the Zariski topology

11 The main theorem

11.1 Statement

11.2 Proof of Theorem 11.1.1: Preparation

11.3 Construction of a relative curve homotopy

11.4 The base homotopy

11.5 The tropical homotopy

11.6 End of the proof

11.7 Variation in families

12 The smooth case

12.1 Statement

12.2 Proof and remarks

13 An equivalence of categories

13.1 Statement of the equivalence of categories

13.2 Proof of the equivalence of categories

13.3 Remarks on homotopies over imaginary base sets

14 Applications to the topology of Berkovich spaces

14.1 Berkovich spaces

14.2 Retractions to skeleta

14.3 Finitely many homotopy types

14.4 More tame topological properties

14.5 The lattice completion

14.6 Berkovich points as Galois orbits

Bibliography

Index

People also search for (Ebook) Non archimedean tame topology and stably dominated types 1st Edition:

tame topology
    
5 basic topology types
    
4 types of topologies
    
4 basic network topologies
    
3 tier topology

Tags: Ehud Hrushovski, François Loeser, Non archimedean, tame topology, stably dominated types