Tate Duality

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.

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.