Statements (22)
| Predicate | Object |
|---|---|
| gptkbp:instanceOf |
gptkb:mathematical_concept
|
| gptkbp:alsoKnownAs |
local-global principle
|
| gptkbp:appliesTo |
gptkb:Diophantine_equations
quadratic forms rational points on varieties |
| gptkbp:describes |
relationship between local and global solvability of equations
|
| gptkbp:field |
gptkb:algebraic_geometry
number theory |
| gptkbp:formedBy |
1920s
|
| gptkbp:generalizes |
gptkb:Chinese_remainder_theorem
|
| gptkbp:hasCounterexample |
certain genus 1 curves
cubic forms in more than 9 variables |
| https://www.w3.org/2000/01/rdf-schema#label |
Hasse principle
|
| gptkbp:namedAfter |
gptkb:Helmut_Hasse
|
| gptkbp:relatedTo |
gptkb:Hasse–Minkowski_theorem
counterexamples such as Selmer curve |
| gptkbp:state |
A rational solution exists if and only if a solution exists in every completion of the rationals
|
| gptkbp:usedIn |
algebraic number theory
arithmetic geometry |
| gptkbp:bfsParent |
gptkb:Helmut_Hasse
gptkb:Algebraic_number_theory |
| gptkbp:bfsLayer |
5
|