[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 65 (1002ﾚｽ)
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497(1): 2022/04/23(土)12:58 ID:MU2asfqc(8/24) AAS
>>496
つづき

In this context, we remark that it is also this state of affairs that gave rise to the term
“inter-universal”: That is to say, 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 of Galois categories
and ´etale topoi associated to schemes. On the other hand, in this mathematics of the
Grothendieck school, typically one only considers relationships between universes ? i.e.,
between labelling apparatuses for sets ? that are induced by morphisms of schemes, i.e.,
in essence by ring homomorphisms. The most typical example of this sort of situation
省8

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498: 2022/04/23(土)12:58 ID:MU2asfqc(9/24) AAS
>>497
つづき

That is to say, it is precisely this sort of situation that is referred to by the term
“inter-universal”. Put another way,
a change of universe may be thought of [cf. the discussion of §2.7, (i)] as
a sort of abstract/combinatorial/arithmetic version of the classical notion
of a “change of coordinates”.
In this context, it is perhaps of interest to observe that, from a purely classical point of
view, the notion of a [physical] “universe” was typically visualized as a copy of Euclidean
three-space. Thus, from this classical point of view,
省3

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