##  [Galois Representation](/galois-representation) 

  ##  [Galois Representation](https://puremath.quantumdictionary.io/galois-representation-0) 

  

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**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

A continuous homomorphism from the absolute Galois group of a field to a matrix group over a topological coefficient ring or field (for example Gal(K̄/K) → GL_n(E)), which linearizes the Galois action and encodes arithmetic information in the language of linear algebra.