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Introduction
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This book deals with non-archimedean tame topology and stably dominated types. It considers o-minimality as an analogy and reduces questions over valued fields to the o-minimal setting. A fundamental tool, imported from stability theory, is the notion of a definable type, which plays a number of roles, starting from the definition of a point of the fundamental spaces. One of the roles of definable types is to be a substitute for the classical notion of a sequence, especially in situations where one is willing to refine to a subsequence. To each algebraic variety V over a valued field K, the book associates in a canonical way a projective limit unit vector V of spaces, which is the stable completion of V. In case the value group is ℝ, the results presented in this book relate to similar tameness theorems for Berkovich spaces.
Title: Introduction
Description:
This book deals with non-archimedean tame topology and stably dominated types.
It considers o-minimality as an analogy and reduces questions over valued fields to the o-minimal setting.
A fundamental tool, imported from stability theory, is the notion of a definable type, which plays a number of roles, starting from the definition of a point of the fundamental spaces.
One of the roles of definable types is to be a substitute for the classical notion of a sequence, especially in situations where one is willing to refine to a subsequence.
To each algebraic variety V over a valued field K, the book associates in a canonical way a projective limit unit vector V of spaces, which is the stable completion of V.
In case the value group is ℝ, the results presented in this book relate to similar tameness theorems for Berkovich spaces.
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