##  [Tame Ramification](/tame-ramification) 

  ##  [Tame Ramification](https://puremath.quantumdictionary.io/tame-ramification-0) 

  

 [![Pure Mathematics Dictionary](/sites/default/files/styles/large/public/2026-01/Pure%20Mathematics.png.webp?itok=5pZnFQ59)](/topic-specific-dictionaries/mathematics-logic/pure-mathematics)

- Mathematics & Logic -

**Pure Mathematics Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Ramification at a prime in an extension of local or global fields for which the ramification index is prime to the residue characteristic p, yielding simpler inertia behavior and absence of nontrivial higher p‑power ramification phenomena.

 

 

 

 

 





 

 



 ##  [Tame Ramification](https://algebra.quantumdictionary.io/tame-ramification-1) 

  

 [![Algebra](/sites/default/files/styles/large/public/2026-01/Algebra.png.webp?itok=3pHxBnUF)](/topic-specific-dictionaries/pure-mathematics/algebra)

- Pure Mathematics -

**Algebra Dictionary**

 







 

 

 

 



 

 

 

 

Definition

Ramification in a finite extension or morphism where the ramification index is prime to the residue characteristic and higher ramification groups vanish; inertia is of order prime to p and local behaviour is controlled and well behaved.