23/01/31 21:28:42.66 FSzGv1IG.net
>>115
>下記ガロア第一論文でも
>”The last application of the theory of equations is related to the modular. equation of elliptic functions.”
>と使われているね
下記 en.wikipedia ”Modular equation”かな？
”geometrically, the n^2-fold covering map from a 2-torus to itself ”
か・・
これ（the n^2-fold covering map）は、下記
望月IUTの"q^j^2"、"同様な同型は楕円曲線のモジュライ・スタック上でも考察することができ"
と関連があるのかもね
(参考)
URLﾘﾝｸ(en.wikipedia.org)
Modular equation
In mathematics, a modular equation is an algebraic equation satisfied by moduli,[1] in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation holding between them, or in other words an identity for moduli.
The most frequent use of the term modular equation is in relation to the moduli problem for elliptic curves. In that case the moduli space itself is of dimension one. That implies that any two rational functions F and G, in the function field of the modular curve, will satisfy a modular equation P(F,G) = 0 with P a non-zero polynomial of two variables over the complex numbers. For suitable non-degenerate choice of F and G, the equation P(X,Y) = 0 will actually define the modular curve.
In that sense a modular equation becomes the equation of a modular curve. Such equations first arose in the theory of multiplication of elliptic functions (geometrically, the n^2-fold covering map from a 2-torus to itself given by the mapping x → n・x on the underlying group) expressed in terms of complex analysis.
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)(2015-02).pdf
宇宙際タイヒミューラー理論への誘（いざな）い 2015-02 望月新一
P4
Hodge-Arakelov 理論
q^j^2
同様な同型は楕円曲線のモジュライ・スタック上でも考察することができ