Background Material from Algebraic Geometry

1991 ◽  
pp. 1-45 ◽  
Author(s):  
Armand Borel
Keyword(s):  
Algebraic Geometry ◽  
Background Material

Some Background Material from Algebraic Geometry

Néron Models ◽  
1990 ◽  
pp. 31-59
Author(s):  
Siegfried Bosch ◽  
Werner Lütkebohmert ◽  
Michel Raynaud
Keyword(s):  
Algebraic Geometry ◽  
Background Material

Preliminaries

2017 ◽  
Author(s):  
Ehud Hrushovski ◽  
François Loeser
Keyword(s):  
Valued Fields ◽  
Definable Set ◽  
Valued Field ◽  
Galois Coverings ◽  
Definable Type ◽  
Definable Sets ◽  
Background Material

This chapter provides some background material on definable sets, definable types, orthogonality to a definable set, and stable domination, especially in the valued field context. It considers more specifically these concepts in the framework of the theory ACVF of algebraically closed valued fields and describes the definable types concentrating on a stable definable V as an ind-definable set. It also proves a key result that demonstrates definable types as integrals of stably dominated types along some definable type on the value group sort. Finally, it discusses the notion of pseudo-Galois coverings. Every nonempty definable set over an algebraically closed substructure of a model of ACVF extends to a definable type.

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