Inter-universal geometry と ABC予想 (応援スレ) 65

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 65 (1002ﾚｽ)
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428: １３２人目の素数さん [] 2022/04/20(水) 08:00:44.09 ID:N6Jzz7Gn

>>427 補足
>京都大学数理解析研究所 教授 望月新一 博士「数学者の中には、宇宙際タイヒミューラー理論が、これまでの数学とは関係ない、別物だという人がいますが、私は、この理論もまた、多くの数学者が研究している数学とつながっていると思っています。数学の世界がつながっているだけでなく、数学者同士もまた、つながっていると信じているのです」

ここ ”デュピー 博士「こんな感じの違和感です。誰かがあるものを持っていて、『それはこれと同じものでもあるし、また同時に異なるものでもある』といったときのような。多くの数学者は、それは『2が4と等しい』といっているようなもので、そんなことをいえば、数学は破綻すると反論したんです」”>>425

ここは、調べてみると、下記のIUTの ”alien”（Mutually Alien Copies）が該当するようだ
単語 ”alien”は、下記のIUT I〜IV の論文PDF内を検索すると、それぞれの論文で、何カ所か出てくるので、4編全部を貫く思想のようです

Mutually Copiesだけなら、同一でしょう？
Mutually Alien Copies とは、何でしょうか？　
『それはこれと同じもの（Mutually Copies）でもあるし、また同時に異なるもの（Alien）でもある』という主張でしょうね

(参考)
https://www.kurims.kyoto-u.ac.jp/~motizuki/papers-japanese.html
望月氏 論文
宇宙際Teichmuller理論
[7] The Mathematics of Mutually Alien Copies: from Gaussian Integrals to Inter-universal Teichmuller Theory. PDF 　　NEW !! (2020-12-23)
https://www.kurims.kyoto-u.ac.jp/~motizuki/Alien%20Copies,%20Gaussians,%20and%20Inter-universal%20Teichmuller%20Theory.pdf

＜追加＞
[1] Inter-universal Teichmuller Theory I: Construction of Hodge Theaters. PDF NEW !! (2020-05-18)
[2] Inter-universal Teichmuller Theory II: Hodge-Arakelov-theoretic Evaluation. PDF NEW !! (2020-12-23)
[3] Inter-universal Teichmuller Theory III: Canonical Splittings of the Log-theta-lattice. PDF NEW !! (2020-05-18)
[4] Inter-universal Teichmuller Theory IV: Log-volume Computations and Set-theoretic Foundations. PDF 　　NEW !! (2020-04-22)
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1644632425/428

497: １３２人目の素数さん [] 2022/04/23(土) 12:58:42.09 ID:MU2asfqc

>>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
is the functor between Galois categories of ´etale coverings induced by a morphism of
connected schemes. By contrast, the links that occur in inter-universal Teichm¨uller
theory are constructed by partially dismantling the ring structures of the rings in their
domains and codomains [cf. the discussion of §2.7, (vii)], hence necessarily result in
much more complicated relationships between the universes ? i.e., between the labelling apparatuses for sets ? that are adopted in the Galois categories that occur in the domains and codomains of these links, i.e., relationships that do not respect the various labelling apparatuses for sets that arise
from correspondences between the Galois groups that appear and the respective
ring/scheme theories that occur in the domains and codomains of the links.

つづく

http://rio2016.5ch.net/test/read.cgi/math/1644632425/497

560: １３２人目の素数さん [] 2022/04/24(日) 10:14:58.09 ID:/7dcPctj

>>558 追加の追加

因みに、” the familiar Galois module “Z＾(1)””とか合ったので下記を引用しておきます

(引用開始)
P17
§ 2.6. Positive characteristic model for mono-anabelian transport
In this example, Galois
groups, or ´etale fundamental groups, in some sense play the role that is played
by tangent bundles in the classical theory - a situation that is reminiscent of the
approach of the [scheme-theoretic] Hodge-Arakelov theory of [HASurI], [HASurII],
which is briefly reviewed in §2.14 below. One notion of central importance in this
example - and indeed throughout inter-universal Teichm¨uller theory! - is the notion
of a cyclotome, a term which is used to refer to an isomorphic copy of some quotient
[by a closed submodule] of the familiar Galois module “Z＾(1)”, i.e., the “Tate twist” of
the trivial Galois module “Z＾”, or, alternatively, the rank one free Z＾-module equipped
with the action determined by the cyclotomic character. Also, if p is a prime number,
then we shall write Z＾=p for the quotient Z＾/Zp.
(引用終り)
以上

http://rio2016.5ch.net/test/read.cgi/math/1644632425/560

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