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In mathematics, Belyi's theorem on algebraic curves states that any non-singular algebraic curve ''C'', defined by algebraic number coefficients, represents a compact Riemann surface which is a ramified covering of the Riemann sphere, ramified at three points only. This is a result of G. V. Belyi from 1979. At the time it was considered surprising, and it spurred Grothendieck to develop his theory of dessins d'enfant, which describes nonsingular algebraic curves over the algebraic numbers using combinatorial data. == Quotients of the upper half-plane == It follows that the Riemann surface in question can be taken to be :''H''/Γ with ''H'' the upper half-plane and Γ of finite index in the modular group, compactified by cusps. Since the modular group has non-congruence subgroups, it is ''not'' the conclusion that any such curve is a modular curve. 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「Belyi's theorem」の詳細全文を読む スポンサード リンク
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