##  [Selmer Group](/selmer-group) 

  ##  [Selmer Group](https://puremath.quantumdictionary.io/selmer-group-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A finite-index subgroup of Galois cohomology classes defined by imposing local conditions that control obstructions to the local-to-global description of rational points on an abelian variety; concretely, the n-Selmer group sits between the n-torsion of the Mordell–Weil group and the global cohomology, providing computable upper bounds on ranks.