Inter-universal geometry と ABC予想 49

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 49 (1002ﾚｽ)
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928: １３２人目の素数さん [sage] 2020/04/14(火) 22:23:40.83 ID:mIlcNUlX

>>924

これか
ここは、SSの文書が公開された当時にも話題になったかも（＾＾

(C1) : Remark 5, “For fixed ... h(P) ? b.”: I can only say that it is a very challenging task to document the depth of my astonishment when I first read this Remark!
This Remark may be described as a breath-takingly  (melo ?) dramatic self-declaration, on the part of SS, of their profound ignorance of the elementary theory of heights, at the advanced undergraduate/beginning graduate level.
Indeed, the finiteness statement at the beginning of the paragraph follows immediately, by considering the j-invariant (say, multiplied by a suitable positive integer N,
which depends only on d and b) of the elliptic curve under consideration, from the finiteness of the set of complex numbers that satisfy a monic polynomial equation of degree d with coefficients ∈ Z of absolute value ? C, for some fixed real number C that depends only on d and b.
To repeat, this sort of argument lies well within the framework of advanced undergraduate/beginning graduate-level mathematics.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1586650355/928

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