[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 49 (1002ﾚｽ)
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555(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)12:55 ID:ZLSkSSTT(20/27) AAS
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Ｐ147
[cf. the discussion preceding [Pano], Theorem 4.1].
(ii) Explicit examples of connections to classical theories: Next, we review
various explicit examples of connections between inter-universal Teichm¨uller theory, as
exposed thus far in the present paper, and various classical theories:
(1cls) Recall from the discussion of §2.10 that the notion of a “universe”, as well as
the use of multiple universes within the discussion of a single set-up in arithmetic
geometry, already occurs in the mathematics of the 1960’s, i.e., in the mathematics
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556: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)12:55 ID:ZLSkSSTT(21/27) AAS
>>555
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Ｐ163
Phenomena that support this point of view of an “atavistic model of mathematical
development” may be seen in many of the examples discussed in §4.1, §4.2, and §4.3
such as the following:
(1atv) The very elementary construction of Belyi maps in the early 1980’s, or indeed
noncritical Belyi maps in [NCBelyi], could easily have been discovered in the
late nineteenth century [cf. §4.3, (i), (5flt); §4.3, (iii), (5PB)].
(2atv) The application of Belyi maps to Belyi cuspidalization [cf. [AbsTopII], §3]
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