1.選択公理の例えは、例えでしかない。その例えが、きちんとIUTの具体的なロジックに適合しているという証明がない限り、数学の議論にはならない (本気で、「きちんとIUTの具体的なロジックに適合しているという証明」が書けるなら、論文にして公開しなよw) 2.ショルツェ氏も同じ。例えば、こういうモノドロミーを考えたら矛盾が起きるという だが、下記のwoitブログでは、Dupuy氏との議論で、”extremely difficult notion of a Hodge theater”とか ”However, these long discussions are all about interpretations. ”と Hodge theaterが難しいからと、解釈に逃げて、最後は ”I’m happy to continue any further discussions by e-mail.”(Peter Scholze says: May 1, 2020 at 4:42 pm)と、裸足で逃げ出す 3.数学の定義と論理は、何通りもの解釈を許さないようにできているもの。「解釈の問題」に逃げ込むのは、なんだかね 4.あと、SS文書のもう一人Stix氏が離脱しかかっていることに、ご注目。 (>>51) Stix氏の離脱がはっきりしたら、SS文書は紙くずですよ。Oberwolfach 7 Mar - 13 Mar 2021 が終われば、はっきりしますよw
(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 0213132人目の素数さん2021/02/24(水) 11:25:40.01ID:eavifJXy>>211 >数学の定義と論理は、何通りもの解釈を許さないようにできているもの。
IUTのホッジシアターが、”extremely difficult notion of a Hodge theater”とか woitブログで白状したのは、ショルツェ氏ですよ なんだ、”notion of a Hodge theater”が分かってない? そりゃ、3.12が分からんはず そもそも、「3.12までは自明だ」と、豪語したのはだれ? 0218132人目の素数さん2021/02/24(水) 17:16:15.38ID:uwykwOBH>>217 >2.そもそも、望月氏はSS文書に逐一反論している。
最後の反論で、Faltings’ theorem (Shafarevich conjecture) applied to the Weil restrictionを通常のFaltings’ theoremと勘違いしたという話があったはず 回答というか講義になってしまうから、SSは回答しなかったんだろう
>IUTのホッジシアターが、”extremely difficult notion of a Hodge theater”とか woitブログで白状したのは、ショルツェ氏ですよ
✨💫✨餅様✨🌟✨ ヴェリ-ミラクル!雨zing!! ∪ァゥェ-サムッ!!! |。○ |=³🐑ゴメンナサ~ィ! 0261132人目の素数さん2021/02/25(木) 20:48:12.92ID:E92Cjw59 V系… ┌───┐ │ ▷ │ └───┘Vㄘゅゥッ!バ- ↗デスナ。 0262132人目の素数さん2021/02/25(木) 21:00:29.35ID: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
なお、下記wikipediaの「幾何オブジェクトのプロパティを基本群のプロパティに減らすことである」は 英文「whose main theme is to reduce properties of geometric objects to properties of their fundamental groups」 の誤訳ですね(”reduce”→「減らす」)
https://en.wikipedia.org/wiki/Neukirch%E2%80%93Uchida_theorem Neukirch–Uchida theorem The Neukirch–Uchida theorem is one of the foundational results of anabelian geometry, whose main theme is to reduce properties of geometric objects to properties of their fundamental groups, provided these fundamental groups are sufficiently non-abelian. 0268132人目の素数さん2021/02/26(金) 00:30:33.23ID:y/io4urq>>266 幸福の科学レベルの見苦しさ。 0269132人目の素数さん2021/02/26(金) 07:07:46.78ID:On93v2bM 積極的に認めようとしない海外の勢力 ってどこですか? ボン大学一派ですか? 0270132人目の素数さん2021/02/26(金) 08:00:06.35ID:64AF3idO>>266 >逆転オセロの始まり始まりぃ〜〜!
どや?😀 0275132人目の素数さん2021/02/26(金) 16:01:45.54ID:/iWCqc/x>>5 南出論文について ”In fact, the estimate in the first display of Corollary C may be strengthened roughly by a factor of 2 by applying the [slightly less elementary] results of [Ink1], [Ink2] [cf. Remarks 5.7.1, 5.8.2].”(下記) とあるので、「まだ改良の余地あり」と読みました
http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文 P5 The proof of Corollary C is obtained by combining • the slightly modified version of [IUTchI-IV] developed in the present paper with • various estimates [cf. Lemmas 5.5, 5.6, 5.7] of an entirely elementary nature.
In fact, the estimate in the first display of Corollary C may be strengthened roughly by a factor of 2 by applying the [slightly less elementary] results of [Ink1], [Ink2] [cf. Remarks 5.7.1, 5.8.2]. [The authors have received informal reports to the effect that one mathematician has obtained some sort of numerical estimate that is formally similar to Corollary C, but with a substantially weaker [by many orders of magnitude!] lower bound for p, by combining the techniques of [IUTchIV], §1, §2, with effective computations concerning Belyi maps. On the other hand, the authors have not been able to find any detailed written exposition of this informally advertized numerical estimate and are not in a position to comment on it.] 0276132人目の素数さん2021/02/26(金) 19:33:17.06ID:64AF3idO>>273 あんたなぁ こんなカキコばっか続けてても 人生のオセロの石 一枚も逆転でけへんよ
南出論文 ”The astronomically large constants in the inequalities established in Theorem 5.3 reflect the explicit [i.e., “non-conjectural”] nature of inter-universal Teichm¨uller theory. ” いやいやいや 確かに、”The astronomically large constants”ですね まだ改善の可能性ありという気がします
http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文
P44 Remark 5.3.1. The astronomically large constants in the inequalities established in Theorem 5.3 reflect the explicit [i.e., “non-conjectural”] nature of inter-universal Teichm¨uller theory. Their size may seem quite unexpected, especially from the point of view of the classical [“conjectural”] literature on such inequalities, where sometimes it is even naively assumed that these constant may be taken to be as small as 1. 0278132人目の素数さん2021/02/26(金) 23:57:37.39ID:xa/RDc+R>>277
南出論文 1. alternative proof ”Fermat’s Last Theorem”、 2.” modularity of elliptic curves over Q and deformations of Galois representations”
確かに、これはこれで、エポックメイキングだが 一方で、”The astronomically large constants”の改善のためには なにか、別の要素とIUTを組み合わせるみたいなこともありかも この場合、その何かが例え” modularity of elliptic curves over Q and deformations of Galois representations”とかであっても、組み合わせは何でもありでしょう
http://www.kurims.kyoto-u.ac.jp/~motizuki/Explicit%20estimates%20in%20IUTeich.pdf Explicit Estimates in Inter-universal Teichmuller Theory. PDF NEW!! (2020-11-30) いわゆる南出論文
P5 The estimate in Corollary C is sufficient to give an alternative proof [i.e., to the proof of [Wls]] of the first case of Fermat’s Last Theorem [cf. Remark 5.8.1].
We also obtain an application of the ABC inequality of Theorem B to a generalized version of Fermat’s Last Theorem [cf. Corollary 5.9], which does not appear to be accessible via the techniques involving modularity of elliptic curves over Q and deformations of Galois representations that play a central role in [Wls]. 0279132人目の素数さん2021/02/27(土) 08:15:01.86ID:f+hU2HEr>>277 追加 下記 「現在、q(a, b, c) > 1.6 を満たす abc-triple は後述の通り3組しか知られていない。q(a, b, c) を 2 まで大きくすれば、そうした abc-triple は存在しないという予想もある。」 「すなわち「全ての abc-triple (a, b, c) に対して、c < rad(abc)2 を満たすであろう」という主張だが、こちらも肯定も否定もされていない[注 4]。」 この「全ての abc-triple (a, b, c) に対して、c < rad(abc)2 を満たすであろう」も、証明できたら良いね そうすれば、フェルマーもスッキリ
注釈 注4^ この主張と元のABC予想の主張の間に論理的な強弱関係はない。 注5^ ABC予想が K = 1 かつ ε = 1 で正しければ、互いに素な自然数 A, B, C が A + B = C を満たすとき C < (rad ABC)2 が成り立つ。互いに素な自然数 a, b, c が an + bn = cn を満たすと仮定すると、an, bn, cn は互いに素より、A = an, B = bn, C = cn を代入して c^n<( rad a^n b^n c^n)^2 が成り立つ。一般に rad x^n= rad x <= x であるから、 ( rad a^n b^n c^n)^2<= (abc)^2<(c^3)^2=c^6 となる。ゆえに c^n < c^6, c > 1 より n < 6。n = 3, 4, 5 については古典的な証明があるので定理が証明される (山崎 2010, p. 11)。 0280132人目の素数さん2021/02/27(土) 08:22:59.30ID:+FXN4YNO 初歩的な線型代数の問題も解けない素人が今日もイキってるね 0281132人目の素数さん2021/02/27(土) 08:54:46.47ID:f+hU2HEr>>279 >「すなわち「全ての abc-triple (a, b, c) に対して、c < rad(abc)2 を満たすであろう」という主張だが、こちらも肯定も否定もされていない[注 4]。」 >この「全ての abc-triple (a, b, c) に対して、c < rad(abc)2 を満たすであろう」も、証明できたら良いね ?そうすれば、フェルマーもスッキリ