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In mathematics, the Lubin–Tate formal group law is a formal group law introduced by to isolate the local field part of the classical theory of complex multiplication of elliptic functions. In particular it can be used to construct the totally ramified abelian extensions of a local field. It does this by considering the (formal) endomorphisms of the formal group, emulating the way in which elliptic curves with extra endomorphisms are used to give abelian extensions of global fields ==Definition of formal groups== Let Z''p'' be the ring of ''p''-adic integers. The Lubin–Tate formal group law is the unique (1-dimensional) formal group law ''F'' such that ''e''(''x'') = ''px'' + ''x''''p'' is an endomorphism of ''F'', in other words : More generally, the choice for ''e'' may be any power series such that :''e''(''x'') = ''px'' + higher-degree terms and :''e''(''x'') = ''x''''p'' mod ''p''. All such group laws, for different choices of ''e'' satisfying these conditions, are strictly isomorphic. We choose these conditions so as to ensure that they reduce modulo the maximal ideal to Frobenius and the derivative at the origin is the prime element. For each element ''a'' in Z''p'' there is a unique endomorphism ''f'' of the Lubin–Tate formal group law such that ''f''(''x'') = ''ax'' + higher-degree terms. This gives an action of the ring Z''p'' on the Lubin–Tate formal group law. There is a similar construction with Z''p'' replaced by any complete discrete valuation ring with finite residue class field, where ''p'' is replaced by a choice of uniformizer. 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「Lubin–Tate formal group law」の詳細全文を読む スポンサード リンク
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