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In mathematics, a Tate module of an abelian group, named for John Tate, is a module constructed from an abelian group ''A''. Often, this construction is made in the following situation: ''G'' is a commutative group scheme over a field ''K'', ''Ks'' is the separable closure of ''K'', and ''A'' = ''G''(''Ks'') (the ''Ks''-valued points of ''G''). In this case, the Tate module of ''A'' is equipped with an action of the absolute Galois group of ''K'', and it is referred to as the Tate module of ''G''. ==Definition== Given an abelian group ''A'' and a prime number ''p'', the ''p''-adic Tate module of ''A'' is : where ''A''() is the ''pn'' torsion of ''A'' (i.e. the kernel of the multiplication-by-''pn'' map), and the inverse limit is over positive integers ''n'' with transition morphisms given by the multiplication-by-''p'' map ''A''() → ''A''(). Thus, the Tate module encodes all the ''p''-power torsion of ''A''. It is equipped with the structure of a Z''p''-module via : 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Tate module」の詳細全文を読む スポンサード リンク
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