[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 65 (1002ﾚｽ)
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496(1): 2022/04/23(土)12:57 ID:MU2asfqc(7/24) AAS
>>495
つづき

P7
§ 1.3. Introduction of identical but mutually alien copies

P12
§ 2. Changes of universe as arithmetic changes of coordinates
§ 2.1. The issue of bounding heights: the ABC and Szpiro Conjectures

In this case, the height of a rational point may
be thought of as a suitable weighted sum of the valuations of the q-parameters of
the elliptic curve determined by the rational point at the nonarchimedean primes of potentially multiplicative reduction [cf. the discussion at the end of [Fsk], §2.2; [GenEll],
省16

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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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