Inter-universal geometry と ABC予想 (応援スレ) 49

Inter-universal geom ..

551:現代数学の系譜雑談
20/10/18 12:54:00.31 ZLSkSSTT.net
>>542
>そうか、この[Alien]っていうのが、重要な論文なんだね～（＾＾
"universe"の説明が詳しいね
以下抜粋する
（参考）
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)
[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory. PDF
　　NEW !! (2020-04-04)
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Contents
§ 2. Changes of universe as arithmetic changes of coordinates
§ 2.10. Inter-universality: changes of universe as changes of coordinates
Ｐ28
It is precisely this state of affairs that results in
the quite central role played in inter-universal Teichm¨uller theory by results in
[mono-]anabelian geometry, i.e., by results concerned with reconstructing
various scheme-theoretic structures from an abstract topological group that “just
happens” to arise from scheme theory as a Galois group/´etale fundamental group.
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
is the functor between Galois categories of ´etale coverings induced by a morphism of
connected schemes.
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