Tate duality

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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[edit]

Main article: local Tate duality

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

\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,Gm).

See also[edit]

References[edit]