0189現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/22(水) 15:17:04.07ID:FY5qB3HE SS Peter Scholze and Jakob Stix は、Taylor Dupuy氏のarXive投稿で、しっかり否定されていますよ ショルツの軍門？ そんなもの Taylor Dupuy氏が、ぶち壊しました（＾＾
（参考） https://www.uvm.edu/~tdupuy/papers.html [ Taylor Dupuy's Homepage]論文集 https://arxiv.org/pdf/2004.13108.pdf Date: April 30, 2020. The Statement of Mochizuki's Corollary 3.12, Initial Theta Data, and the First Two Indeterminacies, (with A. Hilado) (抜粋) P14 Remark 3.8.3. (1) The assertion of [SS17, pg 10] is that (3.3) is the only relation between the q-pilot and Θ-pilot degrees. The assertion of [Moc18, C14] is that [SS17, pg 10] is not what occurs in [Moc15a]. The reasoning of [SS17, pg 10] is something like what follows: (a)～(g)略 (2) We would like to point out that the diagram on page 10 of [SS17] is very similar to the diagram on §8.4 part 7, page 76 of the unpublished manuscript [Tan18] which Scholze and Stix were reading while preparing [SS17]. (3) As of August 1st 2019, the documents above can be found at http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html. We note that there is also the review [Rob 3] which some may find interesting.
[SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017. 1, 1, 1e, 2, 7.5.3 (引用終り) 以上 0190現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/22(水) 15:49:56.91ID:FY5qB3HE "代数曲線の素数pによる還元" （参考） https://ameblo.jp/einstein-1879-314/entry-11156612498.html 私は私の備忘録 2012/02/05 フェルマーの最終定理 ３： フライ曲線の準備 (抜粋) "代数曲線の素数pによる還元"という言葉を定義する必要があります。 Z上の代数曲線F(x,y)=0の素数pによる還元とは、その曲線をZ/pZ（補足参照）で考える事をいいます。
もちろん、愛国というのも深刻な病である ただの暴力団を愛するなどマゾヒストもいいところだし 実際に「暴力団」関係者ならサディストだろう どっちにしても立派な変態である 0213現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/24(金) 08:25:37.88ID:9ZL6gwFd １．SSが、RIMSを訪問して、議論したのが2018年3月 その報告が公表されたのが、[Rpt2018]の”list of revisions”によると、遅くとも2018年10月だ （参考） http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html In March 2018, discussions concerning inter-universal Teichmuller theory (IUTeich) were held at RIMS, Kyoto University. Participation in these discussions was restricted to four mathematicians.
[Rpt2018] Report by Shinichi Mochizuki (with the cooperation of Yuichiro Hoshi) on the March 2018 discussions (updated on 2019-02-01: list of revisions)
２．2018年10月以降で、IUTを認めるという人を挙げると 海外では、Fesenko（＆ W. Porowski（院生））、Dupuy、Joshi 国内では、4月3日の柏原、玉川 東工大 加藤文元、田口雄一郎 望月先生の配下、山下、星、南出 合計 11人
In mathematics, a Frey curve or Frey?Hellegouarch curve is the elliptic curve y^2=x(x-a^ｌ)(x+b^ｌ) associated with a (hypothetical) solution of Fermat's equation a^ｌ+b^ｌ=c^ｌ. The curve is named after Gerhard Frey.
(Gerhard Frey 1982) called attention to the unusual properties of the same curve as Hellegouarch, which became called a Frey curve. This provided a bridge between Fermat and Taniyama by showing that a counterexample to Fermat's Last Theorem would create such a curve that would not be modular. The conjecture attracted considerable interest when Frey (1986) suggested that the Taniyama?Shimura?Weil conjecture implies Fermat's Last Theorem. However, his argument was not complete. In 1985, Jean-Pierre Serre proposed that a Frey curve could not be modular and provided a partial proof of this. This showed that a proof of the semistable case of the Taniyama-Shimura conjecture would imply Fermat's Last Theorem. Serre did not provide a complete proof and what was missing became known as the epsilon conjecture or ε-conjecture. In the summer of 1986, Ribet (1990) proved the epsilon conjecture, thereby proving that the Taniyama?Shimura?Weil conjecture implies Fermat's Last Theorem.
http://scienzamedia.uniroma2.it/~eal/Wiles-Fermat.pdf Annals of Mathematics, 141 (1995), 443-551 Modular elliptic curves and Fermat’s Last Theorem By Andrew John Wiles
Abstract. When Andrew John Wiles was 10 years old, he read Eric Temple Bell’s The Last Problem and was so impressed by it that he decided that he would be the first person to prove Fermat’s Last Theorem. This theorem states that there are no nonzero integers a, b, c, n with n > 2 such that an + bn = cn. The object of this paper is to prove that all semistable elliptic curves over the set of rational numbers are modular. Fermat’s Last Theorem follows as a corollary by virtue of previous work by Frey, Serre and Ribet. 0224現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/25(土) 17:45:36.56ID:kcmyedik>>221 なんでそんなに必死なのかな？君は
お説の根拠は？ｗ 下記に、TAYLOR DUPUY氏の論文の謝辞がある ”Shinichi Mochizuki for his patience in clarifying many aspects of his theory”うんぬんとあって 沢山議論しておりますよｗｗ草草
https://arxiv.org/pdf/2004.13108.pdf PROBABILISTIC SZPIRO, BABY SZPIRO, AND EXPLICIT SZPIRO FROM MOCHIZUKI’S COROLLARY 3.12 TAYLOR DUPUY AND ANTON HILADO Date: April 30, 2020. (抜粋) P4 Acknowledgements. The first author also greatly benefitted from conversations with many other mathematicians and would especially like to thank Yuichiro Hoshi for helpful discussions regarding Kummer theory and his patience during discussions of the theta link and Mochizuki’s comparison; Kirti Joshi for discussions on deformation theory in the context of IUT; Kiran Kedlaya for productive discussions on Frobenioids, tempered fundamental groups, and global aspects of IUT; Emmanuel Lepage for helpful discussions on the p-adic logarithm, initial theta data, aut holomorphic spaces, the log-kummer correspondence,略;
Shinichi Mochizuki for his patience in clarifying many aspects of his theory ? these include discussions regarding the relationship between IUT and Hodge Arakelov theory especially the role of ”global multiplicative subspaces” in IUT, discussions on technical hypotheses in initial theta data; discussions on Theorem 3.11 and ”(abc)-modules”, discussions on mono-theta environments and the interior and exterior cyclotomes, discussions of the behavior of various objects with respect to 略
Chung Pang Mok for productive discussions on the p-adic logarithm, anabelian evaluation, indeterminacies, the theta link, and hodge theaters; Thomas Scanlon for discussions regarding interpretations and infinitary logic as applied to IUT and anabelian geometry. 0226現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/25(土) 18:12:07.97ID:kcmyedik>>221 >次の国際会議は「望月にとって代わる人達」で盛り上がるんでしょう
時枝記事の類似は、2013年12月09日にmathoverflowで、議論されている 二人の数学Dr Alexander Pruss 氏と Tony Huynh氏と、それ以外に質問者Denis氏（彼はコンピュータサインスの人）の周囲の人（"other people argue it's not ok"） たちは、「時枝の議論は測度論的に不成立」と言っている
answered Dec 11 '13 at 21:07 Math Dr. Alexander Pruss 氏 ・・・But we have no reason to think the event of guessing correctly is measurable with respect to the probability measure induced by the random choice of sequence and index i ・・・Intuitively this seems a really dumb strategy.
answered Dec 9 '13 at 17:37 Math Dr. Tony Huynh氏 ・・・If it were somehow possible to put a 'uniform' measure on the space of all outcomes, then indeed one could guess correctly with arbitrarily high precision, but such a measure doesn't exist. 0241１３２人目の素数さん2020/07/26(日) 13:09:46.84ID:9ZaudBKU>>240 え？？？ 同値関係に問題が無い？？？ 問題のある同値関係って例えばどんな同値関係？ で、聞かれてるのは問題の有無じゃなくて、フレシェ・フィルタを用いて定義することはできるか？であって、まったく答えがズレてるんだけど？ もしかしておまえアホ？ 0242現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/07/26(日) 13:22:28.71ID:uQ4z/5zX>>241 時枝の問題では、時枝記事に書かれている同値関係そのままで、問題ないってこと フレシェ・フィルタを用いて同値関係を定義しなおしたら、どんな良いことがあるの？ まさか、不成立の時枝が、成立するとでも？ ＩＩＤ（独立同分布）が反例を構成することは、自明なのにｗ（＾＾； 0243１３２人目の素数さん2020/07/26(日) 14:00:17.78ID:9ZaudBKU>>240 https://mathoverflow.net/questions/151286/probabilities-in-a-riddle-involving-axiom-of-choice What we have then is this: For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n-1)/n. That's right. But now the question is whether we can translate this to a statement without the conditional "For each fixed opponent strategy". ? Alexander Pruss Dec 19 '13 at 15:05 How about describing the riddle as this game, where we have to first explicit our strategy, then an opponent can choose any sequence. then it is obvious than our strategy cannot depend on the sequence. The riddle is "find how to win this game with proba (n-1)/n, for any n." ? Denis Dec 19 '13 at 19:43 But the opponent can win by foreseeing what which value of i we're going to choose and which choice of representatives we'll make. I suppose we would ban foresight of i? ? Alexander Pruss Dec 19 '13 at 21:25 0244１３２人目の素数さん2020/07/26(日) 14:00:44.36ID:9ZaudBKU>>240 >What we have then is this: For each fixed opponent strategy, if i is chosen uniformly independently of that strategy (where the "independently" here isn't in the probabilistic sense), we win with probability at least (n－1)/n. That's right. – Alexander Pruss Dec 19 '13 at 15:05 はい、Pruss も箱入り無数目成立を認めてますよー
>But now the question is whether we can translate this to a statement without the conditional "For each fixed opponent strategy". この question は箱入り無数目とは無関係ですねー
>But the opponent can win by foreseeing what which value of i we're going to choose and which choice of representatives we'll make. Pruss さん正気ですか？予想できたらランダムとは言わないんですよー 負け惜しみはみっともないですねー
https://arxiv.org/pdf/1212.5740.pdf Filters and Ultrafilters in Real Analysis 2012 Max Garcia Mathematics Department California Polytechnic State University
Abstract We study free filters and their maximal extensions on the set of natural numbers. We characterize the limit of a sequence of real numbers in terms of the Fr´echet filter, which involves only one quantifier as opposed to the three non-commuting quantifiers in the usual definition. We construct the field of real non-standard numbers and study their properties. We characterize the limit of a sequence of real numbers in terms of non-standard numbers which only requires a single quantifier as well. We are trying to make the point that the involvement of filters and/or non-standard numbers leads to a reduction in the number of quantifiers and hence, simplification, compared to the more traditional ε, δ-definition of limits in real analysis.
Contents Introduction . . 1 1 Filters, Free Filters and Ultrafilters 3 1.1 Filters and Ultrafilters . . .. 3 1.2 Existence of Free Ultrafilters . . . . . . 5 1.3 Characterization of the Ultrafilter . . . . . . 6 2 The Fr´echet Filter in Real Analysis 8 2.1 Fr´echet Filter . . . . . . . . . 8 2.2 Reduction in the Number of Quantifiers . . .. . . 10 2.3 Fr´echet filter in Real Analysis . . . . . . . 11 2.4 Remarks Regarding the Fr´echet Filter . . . . . 12 3 Non-standard Analysis 14 3.1 Construction of the Hyperreals *R . . . . . 14 3.2 Finite, Infinitesimal, and Infinitely Large Numbers . . . . . . . 16 3.3 Extending Sets and Functions in *R . . . . . . . . . . . . . . . 20 略 A The Free Ultrafilter as an Additive Measure 25
