[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 49 (1002ﾚｽ)
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554(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日)12:55 ID:ZLSkSSTT(19/27) AAS
>>553

つづき

Ｐ50
(i) Types of mathematical objects: In the following discussion, we shall often
speak of “types of mathematical objects”, i.e., such as groups, rings, topological
spaces equipped with some additional structure, schemes, etc. This notion of a “type
of mathematical object” is formalized in [IUTchIV], §3, by introducing the notion of
a “species”. On the other hand, the details of this formalization are not so important
for the following discussion of the notion of multiradiality. A “type of mathematical
object” determines an associated category consisting of mathematical objects of this
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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
>>554
つづき

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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