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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Tate curve ： ウィキペディア英語版 Tate curve In mathematics, the Tate curve is a curve defined over the ring of formal power series $\backslash mathbbq$ with integer coefficients. Over the open subscheme where ''q'' is invertible, the Tate curve is an elliptic curve. The Tate curve can also be defined for ''q'' as an element of a complete field of norm less than 1, in which case the formal power series converge. The Tate curve was introduced by in a 1959 manuscript originally titled "Rational Points on Elliptic Curves Over Complete Fields"; he did not publish his results until many years later, and his work first appeared in . ==Definition== The Tate curve is the projective plane curve over the ring Z of formal power series with integer coefficients given (in an affine open subset of the projective plane) by the equation :$y^2+xy=x^3+a\_4x+a\_6$ where :$-a\_4=5\backslash sum\_n\; \backslash frac\; =\; 5q+45q^2+140q^3+\backslash cdots$ :$-a\_6=\backslash sum\_\backslash frac\backslash times\backslash frac\; =\; q+23q^2+154q^3+\backslash cdots$ are power series with integer coefficients.〔Manin & Panchishkin (2007) p.220〕 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 curve」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.