Non-archimedean tame topology and stably dominated types

Resource Information

The work Non-archimedean tame topology and stably dominated types represents a distinct intellectual or artistic creation found in University of San Diego Libraries. This resource is a combination of several types including: Work, Language Material, Books.

Label

Non-archimedean tame topology and stably dominated types

Statement of responsibility

Ehud Hrushovski, François Loeser

Creator

• Hrushovski, Ehud, 1959-

Contributor

• Loeser, François

Author

• Loeser, François
• Hrushovski, Ehud, 1959-

Subject

• MATHEMATICS -- Topology
• Tame algebras
• Tame algebras
• Electronic books
• MATHEMATICS -- Algebra | Intermediate

Genre

• Electronic books

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

• Annals of mathematics studies, no. 192

Cataloging source

N$T

Index

index present

Language note

In English

Literary form

non fiction

Nature of contents

• dictionaries
• bibliography

Series statement

Annals of mathematics studies

Series volume

number 192