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The complete valued field obtained by completing a field in the metric or uniformity induced by a valuation or absolute value.
wp-completion-at-valuationmilne-algebraic-number-theoryEach relation below ends at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Each place determines a completion of the number field.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
milne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Cauchy completion produces a complete valued field containing a dense image of the original field.
Apply a standard functorial or canonical construction whose output is not merely a reduct of the input and is not generally an equivalent presentation of the same object.
milne-algebraic-number-theoryEach relation below starts at this concept.
This is an authored directed relation from the source endpoint to the target endpoint.
Completing a valued field produces a complete valued field into which the original field maps densely; the completion is unique up to unique isometric isomorphism over the original field.
Pass canonically from a stronger object to structure it determines, or forget part of the data while retaining a valid weaker structure. The carrier may change under a canonical induced construction.
milne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Supply the completion of the base field at the chosen place.
Feed several structures into a construction junction and impose compatibility between them.
milne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
Completing a number field at a non-Archimedean place gives a finite extension of .
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
milne-algebraic-number-theory