Rahul Sharma

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

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

H r ( k , M ) × H 2 r ( k , M ) H 2 ( k , G m ) = Q / Z

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

References

Tate duality Wikipedia


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