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A quadratic form over a number field represents zero nontrivially exactly when it does so over every completion of the field.
wp-hasse-minkowski-theoremmilne-algebraic-number-theorypoonen-rational-points-varietiesEach relation below ends at this concept.
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Hasse–Minkowski is a paradigmatic positive local–global theorem.
A more specific theory, model, entity class, or regime is obtained by restricting or extending the scope of a broader framework.
milne-algebraic-number-theoryThis is an authored directed relation from the source endpoint to the target endpoint.
The Hasse–Minkowski theorem establishes a local–global principle for quadratic forms over number fields.
Record a genuine theorem implication that is not part of the target definition; these edges may point toward a weaker structure.
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Over a number field, the Hasse–Minkowski theorem says that a smooth projective quadric has a rational point if and only if it has a point over every completion; this is the geometric form of local–global isotropy for the defining quadratic form.
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poonen-rational-points-varietiesmilne-algebraic-number-theoryEach relation below starts at this concept.
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