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Valuations
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ALGEBRAIC NUMBER THEORY, A
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Proof of the Weak
Contents
Adelic Viewpoint
Subsections
Valuations
Valuations
Types of Valuations
Examples of Valuations
Topology and Completeness
Topology
Completeness
-adic Numbers
The
-adic Numbers
The
-adic Numbers
Fermat's Last Theorem in
The Field of
-adic Numbers
The Topology of
(is Weird)
The Local-to-Global Principle of Hasse and Minkowski
Weak Approximation
Adic Numbers: The Finite Residue Field Case
Finite Residue Field Case
Normed Spaces and Tensor Products
Normed Spaces
Tensor Products
Extensions and Normalizations of Valuations
Extensions of Valuations
Extensions of Normalized Valuations
Global Fields and Adeles
Global Fields
Restricted Topological Products
The Adele Ring
Strong Approximation
Ideles and Ideals
The Idele Group
Ideals and Divisors
The Function Field Case
Jacobians of Curves
Exercises
William Stein 2008-10-03
