##  [Wild Ramification](/wild-ramification) 

  ##  [Wild Ramification](https://puremath.quantumdictionary.io/wild-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 in an extension of local or global fields at a prime where the ramification index is divisible by the residue characteristic p, producing nontrivial higher ramification groups and more complicated arithmetic and Galois-module structure than the tame case.

 

 

 

 

 





 

 



 ##  [Wild Ramification](https://algebra.quantumdictionary.io/wild-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 occurring in arithmetic or algebraic extensions when higher ramification groups are nontrivial in residue characteristic p dividing the ramification index, producing more complicated, higher-order behaviour than the tame case.