[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 49 (1002ﾚｽ)
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929: 2020/04/14(火)22:24 ID:mIlcNUlX(5/7) AAS
>>928

つづき

It is entirely inconceivable that any researcher with substantial experience working with heights of rational points would attempt to prove this sort of finiteness statement by invoking such a nontrivial result as Faltings’ theorem.
Anyone familiar with the proof of Faltings’ theorem will also recognize immediately that the proof of Faltings’ theorem ultimately reduces to the elementary observation reviewed above, i.e.,
that the finiteness of the set of rational points (of, say, a proper variety) of bounded height over number fields of bounded degree follows immediately from elementary considerations, namely, from the finiteness of the set of solutions of monic polynomial equations of bounded
degree with bounded coefficients ∈ Z.
(Another problem with the argument in Remark 5 is that it is never mentioned why the discriminant of k/Q is bounded.
Such a bound is necessary in order to conclude that the abelian variety A has good reduction outside a fixed finite set of primes that depends only on d and b.)
(引用終り)
以上

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