##  [Local Field Theory](/local-field-theory) 

  ##  [Local Field Theory](https://puremath.quantumdictionary.io/local-field-theory-0) 

  

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- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

The study of local fields — completions of global fields with respect to nontrivial absolute values, such as p-adic fields and local archimedean completions — and their algebraic, topological, and arithmetic structures, including ramification, extensions, and local class field theory.