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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 {{harvs|txt|last=Tate|author-link=John Tate|year=1962}} and {{harvtxt|Poitou|1967}}.
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| ==Local Tate duality==
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| {{main|local Tate duality}}
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| Local Tate duality says there is a perfect pairing of finite groups
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| :<math>\displaystyle H^r(k,M)\times H^{2-r}(k,M')\rightarrow H^2(k,G_m)=Q/Z</math>
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| where ''M'' is a finite group scheme and ''M''′ its dual Hom(''M'',''G<sub>m</sub>'').
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| ==See also==
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| *[[Artin–Verdier duality]]
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| *[[Tate pairing]]
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| ==References==
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| *{{Citation | last1=Haberland | first1=Klaus | title=Galois cohomology of algebraic number fields | url=http://books.google.com/books?id=PwbvAAAAMAAJ | publisher=VEB Deutscher Verlag der Wissenschaften | id={{MR|519872}} | year=1978}}
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| *{{Citation | last1=Poitou | first1=Georges | title=Cohomologie galoisienne des modules finis | url=http://books.google.com/books?id=E3GmAAAAIAAJ | publisher=Dunod | location=Paris | series=Séminaire de l'Institut de Mathématiques de Lille, sous la direction de G. Poitou. Travaux et Recherches Mathématiques, | id={{MR|0219591}} | year=1967 | volume=13 | chapter=Propriétés globales des modules finis | pages=255–277}}
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| *{{Citation | last1=Tate | first1=John | author1-link=John Tate | title=Proceedings of the International Congress of Mathematicians (Stockholm, 1962) | url=http://mathunion.org/ICM/ICM1962.1/ | publisher=Inst. Mittag-Leffler | location=Djursholm | id={{MR|0175892}} | year=1963 | chapter=Duality theorems in Galois cohomology over number fields | pages=288–295}}
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| [[Category:Algebraic number theory]]
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| [[Category:Galois theory]]
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Latest revision as of 15:23, 25 September 2014
I'm Alannah and I live in a seaside city in northern Germany, Blekendorf. I'm 31 and I'm will soon finish my study at Art History.
Feel free to visit my web page Megapolis Hack