Tate duality

In mathematics, Tate duality or Poitou–Tate duality is a duality theorem for Galois cohomology groups of modules over the Galois group of an algebraic number field or local field, introduced by Tate (1962) and Poitou (1967).

Local Tate duality

Main article: local Tate duality

Local Tate duality says there is a perfect pairing of finite groups

Failed to parse (Missing <code>texvc</code> executable. Please see math/README to configure.): \displaystyle H^r(k,M)\times H^{2-r}(k,M')\rightarrow H^2(k,G_m)=Q/Z

where M is a finite group scheme and M′ its dual Hom(M,G_m).

See also

• Artin–Verdier duality
• Tate pairing