＜IUT国際会議 2シリーズ＞ http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/IUT-schedule.html RIMS Promenade in Inter-Universal Teichmuller Theory Org.: Collas (RIMS); Debes, Fresse (Lille). The seminar takes place every two weeks on Thursday for 2 hours by Zoom 17:30-19:30, JP time (9:30-11:30, UK time; 10:30-12:30 FR time) ? we refer to the Programme for descriptions of the talks and associated references.
?? 下記では、abc conjectureから、 "3 Some consequences Roth's theorem on diophantine approximation of algebraic numbers.[5]" となっているぜ なお、[5] Bombieri, Enrico (1994)は、検索ヒットしないが、代わりに ”MACHIEL VAN FRANKENHUYSEN”1998をどぞ
https://en.wikipedia.org/wiki/Abc_conjecture abc conjecture 3 Some consequences ・Roth's theorem on diophantine approximation of algebraic numbers.[5] [5] Bombieri, Enrico (1994). "Roth's theorem and the abc-conjecture". Preprint. ETH Zurich.
http://swc.math.arizona.edu/aws/1998/ The Southwest Center for Arithmetic Geometry Arizona Winter School 1998 http://swc.math.arizona.edu/aws/1998/98ContribA.html Arizona Winter School 1998 Contributed Abstracts Frankenhuysen: abc implies Roth's theorem and Mordell's conjecture By recent work of Elkies (1991), abc implies effective Mordell. And in 1994, Bombieri showed that abc implies Roth's theorem about approximation of an algebraic number by rationals. The proofs of these two theorems are very similar. In this talk, I compare the two proofs. I will also show how a stronger form of Roth's theorem could follow from ABC. http://swc.math.arizona.edu/aws/1998/98Frankenhuysen.pdf THE ABC CONJECTURE IMPLIES ROTH’S THEOREM AND MORDELL’S CONJECTURE MACHIEL VAN FRANKENHUYSEN Abstract. We present in a unified way proofs of Roth’s theorem and an effective version of Mordell’s conjecture, using the ABC conjecture. We also show how certain stronger forms of the ABC conjecture give information about the type of approximation to an algebraic number.
1. Introduction In 1991, Noam D. Elkies showed that the ABC conjecture implies Mordell’s conjecture [5]. And in 1994, Enrico Bombieri showed that the ABC conjecture implies Roth’s theorem about Diophantine approximation of algebraic numbers [3]. The proofs of these two implications are very similar (see §§6.4, 6.7), and in §6.8, we formulate a theorem that implies both Roth’s theorem and Mordell’s conjecture. We formulate the ABC conjecture in §2. In §2.4, we introduce the ‘type function’, which allows us to formulate certain stronger forms of the ABC conjecture.
Roth's theorem is a fundamental result in diophantine approximation to algebraic numbers. It is of a qualitative type, stating that algebraic numbers cannot have many rational number approximations that are 'very good'. Over half a century, the meaning of very good here was refined by a number of mathematicians, starting with Joseph Liouville in 1844 and continuing with work of Axel Thue (1909), Carl Ludwig Siegel (1921), Freeman Dyson (1947), and Klaus Roth (1955).
(>>440-441) https://en.wikipedia.org/wiki/Abc_conjecture abc conjecture 3 Some consequences ・Roth's theorem on diophantine approximation of algebraic numbers.[5] [5] Bombieri, Enrico (1994). "Roth's theorem and the abc-conjecture". Preprint. ETH Zurich.
http://swc.math.arizona.edu/aws/1998/98Frankenhuysen.pdf THE ABC CONJECTURE IMPLIES ROTH’S THEOREM AND MORDELL’S CONJECTURE MACHIEL VAN FRANKENHUYSEN 1. Introduction In 1991, Noam D. Elkies showed that the ABC conjecture implies Mordell’s conjecture [5]. And in 1994, Enrico Bombieri showed that the ABC conjecture implies Roth’s theorem about Diophantine approximation of algebraic numbers [3]. The proofs of these two implications are very similar (see §§6.4, 6.7), and in §6.8, we formulate a theorem that implies both Roth’s theorem and Mordell’s conjecture. 0444現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/13(火) 20:43:54.76ID:Nk0YN5V9>>436 >だから君の言う得られる結果の例にはディオファントス方程式の近似であるトゥエは含まれないだろ
そうか！ おぬし、下記 ディオファントス方程式の ”トゥエ方程式 f (x, y) = k （f (x, y) は3次以上の斉次既約多項式）”と >>443 ”トゥエ＝ジーゲル＝ロスの定理 代数的数のディオファントス近似に関する定理”とを 混同したのかな？ どちらも”トゥエ”が冠されているけどな。別ものだろ！？（＾＾
f(n) = n2 ? n + 41 は、自然数 n が n < 41 で全て素数となる。これは、虚二次体 Q (√{-163}) の類数が 1 であることと関係している[19][20]。一般に、0 ? n < p で多項式 f(n) = n2 ? n + p が素数の値を取るとき、素数 p の値を「オイラーの幸運数」[21] という。オイラーの幸運数は p = 2, 3, 5, 11, 17, 41 の6つのみであり、これらはすべてヘーグナー数と対応する。
多変数多項式 多変数の多項式では、全ての素数を生成することができる式がいくつか知られている。例えば、k + 2 が素数となる必要十分条件は、次のディオファントス方程式が自然数解を持つことである[22]： (引用終り) 以上 0451現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/13(火) 23:19:34.28ID:Nk0YN5V9>>443 >[5] Bombieri, Enrico (1994). "Roth's theorem and the abc-conjecture". Preprint. ETH Zurich.
Enrico Bombieri (born 26 November 1940) is an Italian mathematician, known for his work in analytic number theory, Diophantine geometry, complex analysis, and group theory. He won a Fields Medal in 1974.[5] Bombieri is currently Professor Emeritus in the School of Mathematics at the Institute for Advanced Study in Princeton, New Jersey.[6] 0452現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/13(火) 23:28:13.03ID:Nk0YN5V9>>444 補足 >”トゥエ＝ジーゲル＝ロスの定理
クラウス・フリードリッヒ・ロス（Klaus Friedrich Roth、1925年10月29日 - 2015年11月10日）は、ドイツ出身のイギリスの数学者。ディオファントス近似や不規則偏差理論の研究などで知られる。当時ドイツ領だったブレスラウ（現在はポーランドの都市ヴロツワフ）で生まれ、イギリスで育った。1945年にハロルド・ダヴェンポートの下でケンブリッジ大学のピーターハウス（英語版）を卒業した。
https://ja.wikipedia.org/wiki/%E3%83%AD%E3%82%B9%E3%83%81%E3%83%A3%E3%82%A4%E3%83%AB%E3%83%89%E5%AE%B6 ロスチャイルド家 ロスチャイルド家（Rothschild、「ロスチャイルド」は英語読み。ドイツ語読みは「ロートシルト」。フランス語読みは「ロチルド」[1]。）は、ヨーロッパの財閥、貴族。門閥として名高い。ロマノフ家とはHubert de Monbrison (15 August 1892 ? 14 April 1981) の三度にわたる結婚を介して家族関係にある[2]。また、ベアリング家ともギネス家を介してやはり家族関係である[3]。モルガン家やゴールドシュミット・ファミリーとも親密であり、1001クラブ等の広範なビジネスコネクションをもつ。アメリカについては、ウィルバー・ロスやフィデリティ・インベストメンツと、実業家時代のドナルド・トランプを支援した[4][5]。
https://en.wikipedia.org/wiki/Axel_Thue Axel Thue Axel Thue (Norwegian: ; 19 February 1863 - 7 March 1922), was a Norwegian mathematician, known for his original work in diophantine approximation and combinatorics. Work Thue published his first important paper in 1909.[1] He stated in 1914 the so-called word problem for semigroups or Thue problem, closely related to the halting problem.[2] His only known PhD student was Thoralf Skolem. The esoteric programming language Thue is named after him.
つづく 0456現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 07:37:10.14ID:qOwFO4Cy>>455 つづき https://en.wikipedia.org/wiki/Thue_equation Thue equation In mathematics, a Thue equation is a Diophantine equation of the form ｆ(x,y) = r, where ｆ is an irreducible bivariate form of degree at least 3 over the rational numbers, and r is a nonzero rational number. It is named after Axel Thue who in 1909 proved a theorem, now called Thue's theorem, that a Thue equation has finitely many solutions in integers x and y.[1] The Thue equation is solvable effectively: there is an explicit bound on the solutions x, y of the form {\displaystyle (C_{1}r)^{C_{2}} where constants C1 and C2 depend only on the form ｆ. A stronger result holds, that if K is the field generated by the roots of ｆ then the equation has only finitely many solutions with x and y integers of K and again these may be effectively determined.[2] (引用終り) 以上 0457１３２人目の素数さん2020/10/14(水) 09:04:50.67ID:Sh7FeR3T IUTに直接関係ないこと貼るなよ 0458現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 09:57:24.74ID:WB0JVdoR ５ｃｈは、天下のチラシの裏 便所の落書きともいう 「直接関係ないこと貼るなよ」などは、野暮というもの（＾＾ 0459現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 10:26:48.53ID:WB0JVdoR>>443より http://swc.math.arizona.edu/aws/1998/98Frankenhuysen.pdf THE ABC CONJECTURE IMPLIES ROTH’S THEOREM AND MORDELL’S CONJECTURE MACHIEL VAN FRANKENHUYSEN これ結構面白いわ（＾＾
(抜粋) 1. Introduction in §5, we formulate Mordell’s conjecture and ‘effective Mordell’. §6.3 is devoted to Bely??’s construction of an algebraic function which is ramified over 0, 1 and ∞ alone [1]. The application of this construction to P1 yields Roth’s theorem, §6.4, and the application to a curve C of genus 2 or higher yields Mordell’s conjecture,§6.7.
Both Roth’s theorem and Mordell’s conjecture are theorems, see [10, 16] and [2,4,6,7,21] respectively, and from this point of view it seems uninteresting to have conditional proofs of these theorems, depending on the ABC conjecture, whose validity is still unknown. However, the proofs of these theorems using ABC are much simpler and transparent, and point out very clearly the relationship between the theory of Diophantine approximation and the theory of points on curves of high genus. More importantly, using ABC, one can prove considerably stronger versions of the two theorems. Specifically, ABC implies effective Mordell (see §5.1), and a certain stronger form of the ABC conjecture implies a certain refinement of Roth’s theorem (see §4.1). (引用終り) 以上 0460現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 16:44:09.24ID:WB0JVdoR Kirti Joshi氏は、IUTをperfectoid field に適用しようとしている（＾＾；
https://twitter.com/math_jin math_jin 10月13日 より https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 (抜粋) 1 Introduction I show that one can explicitly construct topologically/geometrically distinguishable data which provide isomorphic copies (i.e. isomorphs) of the tempered fundamental group of a geometrically connected, smooth, quasi-projective variety over p-adic fields. This is done via Theorem 2.3 and Theorem 2.5. Notably Theorem 2.5 also shows that the absolute Grothendieck conjecture fails for the class of Berkovich spaces (over algebraically closed perfectoid fields), arising as analytifications of geometrically connected, smooth, projective variety over p-adic fields. The existence of distinctly labeled copies of the tempered fundamental groups is, as far as I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d], but produced in loc. cit. by entirely different means (for more on this labeling problem see Section 3). Let me also say at the onset that Mochizuki’s Theory does not consider passage to complete algebraically closed fields such as Cp and so my approach here is a significant point of departure from Mochizuki’s Theory . . . and the methods of this paper do not use any results or ideas from Mochizuki’s work. Nevertheless the results presented here establish unequivocally that isomorphs of tempered (and ´etale) fundamental groups, of distinguishable provenance, exist and can be explicitly constructed.
The copies provided by Theorem 2.3 and Theorem 2.5 arise from untilts of a fixed algebraically closed perfectoid field of characteristic p > 0 and hence I call these copies untilts of fundamental groups, or more precisely untilts of tempered fundamental groups.
An important consequence of these results is Corollary 3.1, which provides a function from a suitable Fargues-Fontaine curve to the isomorphism class of the tempered fundamental group of a fixed variety (as above) which provides a natural way of labeling the copies obtained here by closed points of a suitable Fargues-Fontaine curve. In the last section of the paper I show that there is an entirely analogous theory of untilts of topological fundamental groups of connected Riemann surfaces. This note began as a part of another note, [Jos20a], which I put into a limited circulation some time in July 2020, outlining my own approach to some constructions of [Moc12a;Moc12b; Moc12c; Moc12d]. Peter Scholze immediately, but gently, pointed out that the section of [Jos20a], from which the present note is extracted, needed some details. At that time I was readying another note, [Jos20b], for wider circulation and addressing the issue noted by Scholze took longer and on the way I was able to substantially strengthen and clarify my results (which appear here). So ultimately I decided that it would be best to publish the present note separately (while preparation of [Jos20a] continued). My thanks are due to Peter Scholze, and also to Yuichiro Hoshi, Emmanuel Lepage, and Jacob Stix, for promptly providing comments, suggestions or corrections.
2 The main theorem
Lemma 2.1. Let K be a valued field and let R ⊂ K be the valuation ring. The following conditions are equivalent: (1) K is an algebraically closed field, complete with respect to a rank one non-archimedean valuation and with residue characteristic p > 0. (2) K is an algebraically closed, perfectoid field. Proof. A perfectoid field has residue characteristic p > 0 and is complete with respect to a rank one valuation. (引用終り) 以上 0462現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 16:47:56.85ID:WB0JVdoR>>461 >My thanks are due to Peter Scholze, and >also to Yuichiro Hoshi, Emmanuel Lepage, and Jacob Stix, for promptly providing comments, >suggestions or corrections.
https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 (抜粋)
This note began as a part of another note, [Jos20a], which I put into a limited circulation some time in July 2020, outlining my own approach to some constructions of [Moc12a;Moc12b; Moc12c; Moc12d]. Peter Scholze immediately, but gently, pointed out that the section of [Jos20a], from which the present note is extracted, needed some details. At that time I was readying another note, [Jos20b], for wider circulation and addressing the issue noted by Scholze took longer and on the way I was able to substantially strengthen and clarify my results (which appear here). So ultimately I decided that it would be best to publish the present note separately (while preparation of [Jos20a] continued). My thanks are due to Peter Scholze, and also to Yuichiro Hoshi, Emmanuel Lepage, and Jacob Stix, for promptly providing comments, suggestions or corrections.
[Jos20a] Kirti Joshi. “On Mochizuki’s log-link . . .”. In: (2020). In preparation. [Jos20b] Kirti Joshi. “The absolute Grothendieck conjecture is false for Fargues-Fontaine curves”. In: (2020). Preprint. URL: https://arxiv.org/abs/2008.01228. (引用終り)
”At that time I was readying another note, [Jos20b], for wider circulation and addressing the issue noted by Scholze took longer and on the way I was able to substantially strengthen and clarify my results (which appear here). ”とあるな。見落としていたな （＾＾； 0468１３２人目の素数さん2020/10/14(水) 21:03:49.02ID:Sh7FeR3T>>458 他でやれ基地外 0469現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 21:09:46.30ID:qOwFO4Cy>>467 追加
Kirti Joshi氏はすげーな
https://arxiv.org/pdf/2008.01228.pdf The Absolute Grothendieck Conjecture is false for Fargues-Fontaine Curves Kirti Joshi August 5, 2020 (抜粋) 2 The main theorem Let F be an algebraically closed perfectoid field of characteristic p > 0. Let E be a p-adic field i.e. E/Qp is a finite extension. Following [Jos20], I say that two p-adic fields are anabelomorphic if there exists a topological isomorphism GE ? GE′ of their absolute Galois groups; 0470現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 21:10:38.28ID:qOwFO4Cy>>468 で？ なにか？ｗ 0471現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 21:14:22.59ID:qOwFO4Cy>>465 >ちなみにモッチーもパーフェクトイドのお勉強したんだろうな？当然
（>>4より） https://www.math.arizona.edu/~kirti/ から Recent Research へ入る Kirti Joshi Recent Research論文集 Showing 1?44 of 44 results Search v0.5.6 released 2020-02-24 (抜粋) 1.arXiv:2010.05748 [pdf, ps, other] math.AG math.NT Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Authors: Kirti Joshi Submitted 12 October, 2020; originally announced October 2020. Comments: 9 pages
2.arXiv:2008.01228 [pdf, ps, other] math.AG math.NT The Absolute Grothendieck Conjecture is false for Fargues-Fontaine Curves Authors: Kirti Joshi Submitted 3 August, 2020; originally announced August 2020. Comments: 7 pages 0477１３２人目の素数さん2020/10/14(水) 22:30:56.62ID:Sh7FeR3T>>472 レベル低すぎなんだよ もっと勉強してから来い 0478現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/14(水) 23:53:37.20ID:qOwFO4Cy>>477 意味わかんねー あんたの書いたこと、どれ？ どれだけレベル高いことを書いたのかな？ 示してみなよ（＾＾；
・ Henri Darmon: Frey’s method and hyperelliptic curves with real multiplication http://swc.math.arizona.edu/aws/1998/98Darmon.pdf Rigid local systems, Hilbert modular forms, and Fermat’s last theorem Henri Darmon March 3, 1999 0480現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木) 11:23:16.75ID:esT5rSCm>>467 追加 https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 (抜粋) 1 Introduction
The existence of distinctly labeled copies of the tempered fundamental groups is, as far as I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d], but produced in loc. cit. by entirely different means (for more on this labeling problem see Section 3). Let me also say at the onset that Mochizuki’s Theory does not consider passage to complete algebraically closed fields such as Cp and so my approach here is a significant point of departure from Mochizuki’s Theory . . . and the methods of this paper do not use any results or ideas from Mochizuki’s work. Nevertheless the results presented here establish unequivocally that isomorphs of tempered (and ´etale) fundamental groups, of distinguishable provenance, exist and can be explicitly constructed.
An important consequence of these results is Corollary 3.1, which provides a function from a suitable Fargues-Fontaine curve to the isomorphism class of the tempered fundamental group of a fixed variety (as above) which provides a natural way of labeling the copies obtained here by closed points of a suitable Fargues-Fontaine curve. In the last section of the paper I show that there is an entirely analogous theory of untilts of topological fundamental groups of connected Riemann surfaces.
3 Untilts of tempered fundamental groups The results of the preceding section can be applied to the problem of producing labeled copies of the tempered fundamental groups. A simple example of the labeling problem is the following: let G be a topological group isomorphic to the absolute Galois group of some p-adic field. In this case one can ask if there are any distinguishable elements in the topological isomorphism class of G with the distinguishing features serving as labels. 0481現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木) 11:26:18.33ID:esT5rSCm>>480 補足
”Let me also say at the onset that Mochizuki’s Theory does not consider passage to complete algebraically closed fields such as Cp and so my approach here is a significant point of departure from Mochizuki’s Theory . . . and the methods of this paper do not use any results or ideas from Mochizuki’s work. ”
https://en.wikipedia.org/wiki/Siegel_zero Siegel zero (抜粋) In mathematics, more specifically in the field of analytic number theory, a Siegel zero, named after Carl Ludwig Siegel, is a type of potential counterexample to the generalized Riemann hypothesis, on the zeroes of Dirichlet L-function. Importance The importance of the possible Siegel zeroes is seen in all known results on the zero-free regions of L-functions: they show a kind of 'indentation' near s = 1, while otherwise generally resembling that for the Riemann zeta function ? that is, they are to the left of the line Re(s) = 1, and asymptotic to it. Because of the analytic class number formula, data on Siegel zeroes have a direct impact on the class number problem, of giving lower bounds for class numbers. This question goes back to C. F. Gauss. Work on the class number problem has instead been progressing by methods from Kurt Heegner's work, from transcendental number theory, and then Dorian Goldfeld's work combined with the Gross-Zagier theorem on Heegner points.
https://dms.umontreal.ca/~andrew/PDF/NoSiegelfinal.pdf Granville, Andrew; Stark, H. (2000). “ABC implies no "Siegel zeros" for L-functions of characters with negative exponent”. Inventiones Mathematicae 139: 509?523. (抜粋) Introduction.Oesterl he and Masser's abc-conjecture asserts that for any given Р > 0, if a, b andc are coprime positive integers satisfying a + b = c then 以上 0498現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/16(金) 11:35:32.79ID:e3ApkVhO (これは、ジーゲル零点とは関係ないが、abcの気楽な読み物として) http://www.ams.org/notices/200210/fea-granville.pdf Granville, Andrew; Tucker, Thomas (2002). “It’s As Easy As abc”. Notices of the AMS 49 (10): 1224?1231. (抜粋) Fermat’s Last Theorem In this age in which mathematicians are supposed to bring their research into the classroom, even at the most elementary level, it is rare that we can turn the tables and use our elementary teaching to help in our research. However, in giving a proof of Fermat’s Last Theorem, it turns out that we can use tools from calculus and linear algebra only. This may strike some readers as unlikely, but bear with us for a few moments as we give our proof. 0499現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/16(金) 12:06:11.74ID:e3ApkVhO ピエール松見氏、面白そう（＾＾ https://staff.aist.go.jp/t-yanagisawa/activity/seminar.html 柳澤 孝 Takashi Yanagisawa 産業技術総合研究所（AIST） https://staff.aist.go.jp/t-yanagisawa/activity/matsumi.pdf January 29, 2013 From 15:00 Tsukuba Central 2 M304 ピエール松見氏（チェンナイ数理科学研究所（インド））: 楕円曲線と数論- ABC予想の現状 -
https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 （翻訳）＜www.DeepL.com/Translator（無料版）の翻訳に手を入れた＞ このノートは、私が2020年7月頃に限定的に回覧した別のノート[Jos20a]の一部として始まったもので、[Moc12a;Moc12b;Moc12c;Moc12d]のいくつかの解釈に対する私自身のアプローチを概説したものである。 Peter Scholzeはすぐに、しかし優しく、このノートが抜粋されている[Jos20a]の部分には詳細が必要だと指摘した。 そこで、私は別のノート[Jos20b]を準備し、より広く回覧するために私は自分の結果を大幅に強化し、Scholzeが指摘した問題への対処に時間をかけて、明確にすることができました（それがここに掲載されています）。 そのため，最終的には（[Jos20a] の準備を続けながら）本ノートとは別に出版した方が良いと判断しました．Peter Scholze氏と、コメント、提案、修正を迅速に提供してくれた星裕一氏、Emmanuel Lepage氏、Jacob Stix氏に感謝します。 （訳の終り）
これから分かることは、 ・Kirti Joshi ノート[Jos20a]を、「限定的に回覧」（which I put into a limited circulation）した。 ・別のノート[Jos20b]を、「より広く回覧」（for wider circulation） ・Peter Scholze氏、Jacob Stix氏に感謝します（My thanks are due to Peter Scholze, Jacob Stix,for promptly providing comments,suggestions or corrections.） ・だから、今年４月から５月のwoitブログの時からは、大分議論は変わってきて、Kirti Joshi の仕事が、IUTとパーフェクトイドとを融合する役割をしているように思う ・Peter Scholze氏とJacob Stix氏とも、Kirti Joshi の仕事を認めている
今後も、こういう動きが、どんどん出てくるように思います（＾＾ 0503１３２人目の素数さん2020/10/16(金) 21:58:15.30ID:0pOLigpq>>502 その論文に"the methods of this paper do not use any results or ideas from Mochizuki’s work"ってはっきり書いてあるんだけど、いったいどこに目を付けてんの？ ideasさえ使ってないって言ってるよ 0504１３２人目の素数さん2020/10/16(金) 22:09:31.86ID:ZepuYihq>>503 お前高卒だろ？この英訳でさえもまる反対の意味にとるとはアホ丸出し 0505現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/16(金) 23:58:42.89ID:w2Iu7oDW>>503-504 まあまあ そう焦らずに
もう少し長い目で見ていれば だんだん分かってくるよ、何が正しいか（＾＾；
4月のＲＩＭＳの記者会見 それを受けてのwoitでの議論があり
いま10月だから半年経過して いま Kirti Joshi の論文が出た
世の中徐々に動いているってことです アンチの言っていることとは、別の方向へね 0506現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/16(金) 23:59:56.80ID:w2Iu7oDW （>>4より） 山下剛サーベイ http://www.kurims.kyoto-u.ac.jp/~gokun/DOCUMENTS/abc2019Jul5.pdf A proof of the abc conjecture after Mochizuki.preprint. Go Yamashita last updated on 8/July/2019. (抜粋) Ｐ3 § 0. Introduction. The author once heard the following observation, which was attributed to Grothendieck: There are two ways to crack a nut ? one is to crack the nut in a single stroke by using a nutcracker; the other is to soak it in water for an extended period of time until its shell dissolves naturally. Grothendieck’s mathematics may be regarded as an example of the latter approach.
A similar statement can be made concerning S. Mochizuki’s proof of the abc Conjecture. (引用終り)
１．ＩＵＴアンチ、特に維新さん、些末なことを針小棒大に妄想して、IUT不成立を主張する いわく、玉川が（審査過程を）「墓場まで持っていく」といったから、「審査でずるしている」とかね ２．しかしながら、数学での論文査読パスは、一次審査でしかない その後、各人の数学者たちが、日常の研究活動の中で、不断の検証とそれをさらに発展させる研究を通じて、その論文の正しさが確立されていくべきものです ３．数学の論文は、教典ではない。どんな大論文であれ、一つの通過点でしかない さらに高い立場と視点から、論文の正しさが、何度も繰返し検証されていくものです ４． Kirti Joshi 氏が、やったこと、やろうとしていることは、正にそれ(>>502) ノート[Jos20a]で、[Moc12a;Moc12b;Moc12c;Moc12d]のいくつかの解釈に対する彼自身のアプローチを概説した それを仲間内に回覧したところ、Peter Scholze氏から指摘があって、そこを補強した。それが、この論文だという(>>502) ５．重要なポイントは、Kirti Joshi 氏は、望月IUT [Moc12a;Moc12b;Moc12c;Moc12d]は正しいと思っているわけ で、彼自身の独自の手法での解釈アプローチをしたってこと 彼の手法は、IUTとはまた別だという。特にラベル付けの部分でね （ ”I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d], but produced in loc. cit *). by entirely different means (for more on this labeling problem see Section 3). ”（>>480）) ６．ご存知と思うが、この”ラベル付け”問題が、SSからの指摘で取り上げられていた ７．そんなこんなで、いま４月のRIMSの記者会見から半年経って、上記のKirti Joshi 氏とか、Promenade in IUT(>>419)とか、IUTを消化吸収して数学を進めていこうという動きが出ている そして、来年は４つのIUT国際会議があるのです ８．IUTの数学は、着実に前進しているのです
女史は、「I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d]」とか 「As far as I understand this problem was considered, and solved (in many cases of interest) by Mochizuki in [Moc12a; Moc12b; Moc12c; Moc12d].」とか あるよ
（>>508） ”I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d], but produced in loc. cit *). by entirely different means (for more on this labeling problem see Section 3). ”（>>480） https://arxiv.org/pdf/2010.05748.pdf Untilts of fundamental groups: construction of labeled isomorphs of fundamental groups Kirti Joshi October 13, 2020 (抜粋)
I understand, crucial to [Moc12a; Moc12b; Moc12c; Moc12d], but produced in loc. cit. by entirely different means (for more on this labeling problem see Section 3).
P5 3 Untilts of tempered fundamental groups
So one may again ask: is it possible to provide copies of Π which are labeled by geometrically/topologically distinguishable labels? As far as I understand this problem was considered, and solved (in many cases of interest) by Mochizuki in [Moc12a; Moc12b; Moc12c; Moc12d]. Theorem 2.5 provides a different solution to this problem. 0513現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/17(土) 10:03:07.25ID:02Kfs2KS>>507 ”ガウスの数論論文集に寄せて17. 「4次剰余の理論」より この論文では、複素数に関する基本事項とともに、4次剰余の理論のはじまりの部分を確立する。全容を展開するのは、これから引き続いて行うことにしたいと思う。> ここで語られているのは、数論に複素数が導入されたときの一番はじめの情景です。論文の中で「複素数に関する基本事項」が叙述されますが、そこには今日のいわゆる複素平面も登場します。数学にどうして複素数を導入しなければならないのかというと、4次剰余に関する諸定理が「際立った簡明さと真正の美しさをもって明るい光を放つ」ようにするためというのですが、複素数というものの実在感をこれほど雄弁に物語るものはなく、「自乗したら負になる数」はあるのかないのかなどという疑問はまったく問題になりません。”
（参考） http://www.kurims.kyoto-u.ac.jp/~motizuki/research-japanese.html 望月 過去と現在の研究 ・南出新氏による、IUTeichにおける明示的な不等式に関する講演のスライドを掲載 http://www.kurims.kyoto-u.ac.jp/~motizuki/Minamide%20---%20Explicit%20estimates%20in%20inter-universal%20Teichmuller%20theory%20(in%20progress).pdf Explicit estimates in inter-universal Teichm¨uller theory (in progress) (joint work w/ I. Fesenko, Y. Hoshi, S. Mochizuki, and W. Porowski) Arata Minamide RIMS, Kyoto University November 2, 2018
https://www.maths.nottingham.ac.uk/plp/pmzibf/mp.html Ivan Fesenko - Research in texts ・[R3] Sh. Mochizuki, I. Fesenko, Yu. Hoshi, A. Minamide, W. Porowski, Explicit estimates in inter-universal Teichmuller theory, work in progress, talk in 2018, talk in 2020 https://events.goettingen-campus.de/event?eventId=20836 From Teichmuller to Mochizuki: arithmetic-anabelian IUT, its effective version and applications 23.1.2020, 0526ぷっちゃん2020/10/18(日) 08:05:55.89ID:QA1+6emM>>523 まったくだ
http://www.kurims.kyoto-u.ac.jp/~bcollas/IUT/documents/RIMS-Lille%20-%20Promenade%20in%20Inter-Universal%20Teichm%C3%BCller%20Theory.pdf PROMENADE IN INTER-UNIVERSAL TEICHMULLER THEORY - 復元 Online Seminar - Algebraic & Arithmetic Geometry Laboratoire Paul Painleve - Universite de Lille, France
P3 Modus Operandi & Leitfaden. As a new geometry, the essence of Mochizuki’s IUT is to introduce a new semiotic system - formalism, terminology, and their interactions - that can be unsettling at first. This programme proposes a 3 layers approach with precise references, examples, and analogies. Because IUT discovery also benefits from a non-linear and spiralling approach, we provide further indications for an independent wandering: Mochizuki recommends to start with the introductory [Alien] - young arithmetic-geometers can also consult [Fes15] for a shorter overview. We also recommend to begin with §Intro - §3.6-7 ibid. for a direct encounter with IUT’s semiotic, then to follow one’s own topics of interest according to Fig. 1, which also indicates some topic-wise references as entry-points - [EtTh], [GenEll], etc. Within the “canon” [IUTChI]-[IUTChIV], our recommendation is to start with [IUTChIII] §Introduction. Intuition of the reader can further rely on the strongly consistent terminology of IUT - e.g. Frobenioid, mono-anabelian transport, arithmetic analytic.
※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.
※ Hodge-Arakelov and p-adic Teichmuller theories stand as important models for IUT, which also relies on key categorical constructions - e.g. Frobenioids and anabelioids. These aspects are not included in this programme - we refer to [Alien] and the canon for references - they can be the object of additional talks by specialists. 以上 0533現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/18(日) 10:52:02.83ID:ZLSkSSTT>>532 補足 >※ We have also found the synthetic and selfcontent [Yam17] to be particularly helpful as a bridge between [Alien] and the “canon”.
