Interｰuniversal geometryとABC予想(応用スレ)51

[過去ﾛｸﾞ] Interｰuniversal geometryとABC予想(応用スレ)51 (1002ﾚｽ)
上下前次1-新
通常表示 512ﾊﾞｲﾄ分割ﾚｽ栞
抽出解除必死ﾁｪｯｶｰ(本家) (べ) 自ID ﾚｽ栞あぼーん

このｽﾚｯﾄﾞは過去ﾛｸﾞ倉庫に格納されています｡
次ｽﾚ検索歴削→次ｽﾚ栞削→次ｽﾚ過去ﾛｸﾞﾒﾆｭｰ

675: １３２人目の素数さん [] 2021/02/18(木) 14:44:23.44 ID:qnnVeZy1

>>673
>それだけの時間をかけても、誰もCor 3.12の証明を追記できなかったということだな

Cor 3.12の証明は、大幅にリバイズされているよ
ファイルの変更履歴を見てください。確か、A4で１頁くらい増えたと思うよ

＞そして証明が変わってないのだから、理解できないことも変わらない

証明の本質は変わってないだろうが、分かり易くしたらしい
加藤文元先生が、IUTの証明はだいぶ分かり易くなったとか、どこかで発言していたよ

＞Cor 3.12の証明の論理的な飛躍が指摘されているのに誰も埋められない、これが全て

「論理的な飛躍が指摘されている」の部分が、違うよ
ショルツ氏の指摘は、「IUTで、こういうモノドロミーを考えると、矛盾が起きる」という指摘だよね
で、Dupuy氏の見解は、「そのモノドロミー（の反例？）は、IUTとは関係ない」という説明です（彼のwoitブログ発言、及びarXive投稿論文）
望月先生「根本的に、学部生か院生なみの勘違いがある」という説明です

（>>672再録）
http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html
2018年3月、数理研で行なわれたIUTeichに関する議論を纏めた報告書　（および関連文書）
http://www.kurims.kyoto-u.ac.jp/~motizuki/protectedpdf-2018-08/SS2018-08.pdf
Why abc is still a conjecture
PETER SCHOLZE AND JAKOB STIX Date: August 23, 2018.
P10
Thus, Mochizuki wanted to introduce scalars of j2 somewhere on the left part of this
diagram (which strictly speaking leads to inconsistencies, i.e. monodromy, on the left part of the
diagram alone, which arguably can be overcome by using averages). However, it is clear that
this will result in the whole diagram having monodromy j2, i.e., being inconsistent.
The conclusion of this discussion is that with consistent identifications of copies of real numbers, one must in (1.5) omit the scalars j2 that appear, which leads to an empty inequality.

http://rio2016.5ch.net/test/read.cgi/math/1610452199/675

679: １３２人目の素数さん [] 2021/02/18(木) 15:25:43.14 ID:qnnVeZy1

>>677
うーん、あなたは誠実だね

＞確かにショルツが初めてCor 3.12の証明を指摘してからは若干追記されてるが、査読が終わりブログで取り上げられた2020年4月ごろにショルツがまだ証明されたと思っていないと明言してから追記されていない

細かくフォローできていないが、それ昨年4月の査読完了のプレス発表を受けて、woitブログにショルツ氏が登場したときだよね
で、彼はIUT論文の改訂など細かい話には、首を突っ込んでいないみたいだよ

>その前にまずCor 3.12が証明されてないという指摘があって、
>その上でCor 3.12は成り立たないだろうと指摘してる

その話は、woitブログでの最後、Dupuy氏に対するコメントで分かるけど
”Cor 3.12が証明されてない”と”Cor 3.12は成り立たないだろう”とは、表裏一体と見ました

（参考）
https://www.math.columbia.edu/~woit/wordpress/?p=11709
Not Even Wrong Latest on abc April 3, 2020 by woit
Peter Scholze April 30, 2020
Dear Taylor,
Reading the IUT papers, however, you are presented with some extremely difficult notion of a Hodge theater, together with a highly non-obvious notion of isomorphisms of such: Isomorphisms do not preserve nearly as much structure as you would expect them to, and this is by design as Mochizuki points out. So I find it very hard to “guess” what something like a surrounding “theory” might be. For all I can see, Hodge theaters fit neither into the framework of “structures” as used in the wikipedia entry https://en.wikipedia.org/wiki/Interpretation_(model_theory) you linked to, nor the topos-theoretic framework of Caramello. (Regarding the first one: A “structure” in the sense of model theory has first of all an underlying set. I find it hard to take a Hodge theater and produce some interesting set that is functorial in isomorphisms of Hodge theaters, the problem being the very lax notion of isomorphisms of Hodge theaters.)

つづく

http://rio2016.5ch.net/test/read.cgi/math/1610452199/679

680: １３２人目の素数さん [] 2021/02/18(木) 15:26:38.29 ID:qnnVeZy1

>>679
つづき

However, these long discussions are all about interpretations. Regarding the mathematics proper: I stand by the claim made in our manuscript, and have indicated the proof above.
Best wishes!
Peter

Peter Scholze says:
May 1, 2020 at 4:42 pm
Dear Taylor,
thanks for your further comments. I think W said it all.
Let me just make the following clarification regarding (1).
略
Actually, in the context of the current thread, it would have been a good question whether, given that a Hodge theater is a collection of certain topological groups isomorphic to
’s for certain different ’s, plus other data, with lots of relations, can you actually interpret all those things as some convenient structure on the side of schemes again? This is not a priori clear, and Mochizuki’s central claim is that by passing to
’s, he can do interesting new things. So he cooks up a Hodge theater. And … you can beautifully interpret it in good old schemes, it “is” just a curve over your original number field .
The same happens for everything else I’ve seen in IUT or your comments.
I’m happy to continue any further discussions by e-mail.
Best wishes!
Peter

http://rio2016.5ch.net/test/read.cgi/math/1610452199/680

682: １３２人目の素数さん [] 2021/02/18(木) 16:22:28.11 ID:qnnVeZy1

>>679-680
>Reading the IUT papers, however, you are presented with some extremely difficult notion of a Hodge theater, together with a highly non-obvious notion of isomorphisms of such: Isomorphisms do not preserve nearly as much structure as you would expect them to, and this is by design as Mochizuki points out. So I find it very hard to “guess” what something like a surrounding “theory” might be. For all I can see, Hodge theaters fit neither into the framework of “structures” as used in the wikipedia entry https://en.wikipedia.org/wiki/Interpretation_(model_theory) you linked to, nor the topos-theoretic framework of Caramello. (Regarding the first one: A “structure” in the sense of model theory has first of all an underlying set. I find it hard to take a Hodge theater and produce some interesting set that is functorial in isomorphisms of Hodge theaters, the problem being the very lax notion of isomorphisms of Hodge theaters.)
>However, these long discussions are all about interpretations. Regarding the mathematics proper: I stand by the claim made in our manuscript, and have indicated the proof above.

これ読むと、 IUTは難しいこと一杯書いてあって、その解釈も難しい
”some extremely difficult notion of a Hodge theate”とか、「あれあれ？？」ってこと書いてあるよね
でも、要するに、「おれ（ショルツ氏）は、主張を変えないよ！」ってことでしょ

で、”The same happens for everything else I’ve seen in IUT or your comments.
I’m happy to continue any further discussions by e-mail.”
だって。ショルツ氏から議論を打ち切ったから、もうショルツ氏は良いんじゃない？

http://rio2016.5ch.net/test/read.cgi/math/1610452199/682

上下前次1-新書関写板覧索設栞歴

ｽﾚ情報赤ﾚｽ抽出画像ﾚｽ抽出歴の未読ｽﾚ AAｻﾑﾈｲﾙ

ぬこの手ぬこTOP 0.030s