##  [Local–Global Principle](/local-global-principle) 

  ##  [Local–Global Principle](https://puremath.quantumdictionary.io/local-global-principle-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A heuristic and often formal assertion in arithmetic and algebraic contexts that a global property of an object (over a global field or ring) holds precisely when the corresponding property holds in every relevant local completion or localization; concretely, a global solvability, isomorphism class, or cohomological vanishing is equivalent to the collection of its local counterparts satisfying the