##  [Tate Duality](/tate-duality) 

  ##  [Tate Duality](https://puremath.quantumdictionary.io/tate-duality-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

A family of canonical pairings between Galois cohomology groups of local or global fields, typically pairing H^i(G_K, M) with H^{2-i}(G_K, M^*) (or their analogues), that identify arithmetic invariants and dualize obstructions for finite Galois modules and related coefficients.

 

 

 

 

 





 

 



 ##  [Tate Duality](https://algebra.quantumdictionary.io/tate-duality-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

A family of duality theorems in Galois cohomology that provide perfect pairings between cohomology groups of a Galois module and those of its Pontryagin dual (often with Tate twists), for local and global fields; local Tate duality is a cornerstone of arithmetic duality theory.