Inter-universal geometry と ABC予想 (応援スレ) 52

[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 52 (1002ﾚｽ)
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212: １３２人目の素数さん [] 2021/02/24(水) 11:06:15.19 ID:PXsEolJh

>>211
つづき

（参考）
https://www.math.columbia.edu/~woit/wordpress/?p=11709
（woitブログ）
Not Even Wrong Latest on abc Posted on April 3, 2020 by woit

Peter Scholze says:
April 30, 2020 at 3:32 am

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.
（終わり）
以上

http://rio2016.5ch.net/test/read.cgi/math/1613784152/212

262: １３２人目の素数さん [] 2021/02/25(木) 21:00:29.35 ID:pYr0FQSU

>>212
(引用開始)
https://www.math.columbia.edu/~woit/wordpress/?p=11709
（woitブログ）
Not Even Wrong Latest on abc Posted on April 3, 2020 by woit
Peter Scholze says:
April 30, 2020 at 3:32 am
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.
（終わり）

ショルツェ氏は、「Cor3.12までは、自明なことしか書いていない」と言いながら
”some extremely difficult notion of a Hodge theater”とのたまう

あれあれ？　
「Cor3.12までは、自明なことしか書いていない」んじゃないの？

まあ、”Hodge theater”が分からないなら
Cor3.12の証明が分からなくても不思議なし！！

http://rio2016.5ch.net/test/read.cgi/math/1613784152/262

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