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In mathematics, Hodge–Arakelov theory of elliptic curves is an analogue of classical and ''p''-adic Hodge theory for elliptic curves carried out in the framework of Arakelov theory. It was introduced by . Mochizuki's main comparison theorem in Hodge–Arakelov theory states (roughly) that the space of polynomial functions of degree less than ''d'' on the universal extension of a smooth elliptic curve in characteristic 0 is naturally isomorphic (via restriction) to the ''d''2-dimensional space of functions on the ''d''-torsion points. It is called a comparison theorem as it is an analogue for Arakelov theory of comparison theorems in cohomology relating de Rham cohomology to singular cohomology of complex varieties or étale cohomology of ''p''-adic varieties. In and he pointed out that arithmetic Kodaira-Spencer map and Gauss-Manin connection may give some important hints for Vojta's conjecture, ABC conjecture and so on. ==References== * * * 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「Hodge–Arakelov theory」の詳細全文を読む スポンサード リンク
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