✨💫✨餅様✨🌟✨ ｳﾞｪﾘ-ﾐﾗｸﾙ!雨zing!! ∪ｧｩｪ-ｻﾑｯ!!! |。○ |=³🐑ｺﾞﾒﾝﾅｻ~ｨ! 0261１３２人目の素数さん2021/02/25(木) 20:48:12.92ID:E92Cjw59 V系… ┌───┐ │ ▷ │ └───┘Vㄘゅｩｯ!ﾊﾞ- ↗ﾃﾞｽﾅ。 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
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 P2 Introduction
Theorem. 7We shall regard X as the “λ-line” - i.e., we shall regard the standard coordinate on X as the “λ” in the Legendre form “y2 = x(x-1)(x-λ)” of the Weierstrass equation defining an elliptic curve -
P34 Corollary 5.2. (Construction of suitable µ6-initial Θ-data) Write X for the projective line over Q; D ⊆ X for the divisor consisting of the three points “0”, “1”, and “∞”; (Mell)Q for the moduli stack of elliptic curves over Q. We shall regard X as the “λ-line” - i.e., we shall regard the standard coordinate on X as the “λ” in the Legendre form “y2 =x(x - 1)(x - λ)” of the Weierstrass equation defining an elliptic curve - 0302１３２人目の素数さん2021/02/27(土) 12:51:48.66ID:f+hU2HEr>>301 >the Legendre form >ここらが重要キーワードですね
The respective complete elliptic integrals are obtained by setting the amplitude, Φ, the upper limit of the integrals, to π/2.
The Legendre form of an elliptic curve is given by y2 = x(x-1)(x-λ)
Numerical evaluation The classic method of evaluation is by means of Landen's transformations. Descending Landen transformation decreases the modulus k k towards zero, while increasing the amplitude Φ. Conversely, ascending transformation increases the modulus towards unity, while decreasing the amplitude. In either limit of k, zero or one, the integral is readily evaluated.
Most modern authors recommend evaluation in terms of the Carlson symmetric forms, for which there exist efficient, robust and relatively simple algorithms. This approach has been adopted by Boost C++ Libraries, GNU Scientific Library and Numerical Recipes.[3] 0303１３２人目の素数さん2021/02/27(土) 13:31:25.71ID:+FXN4YNO>>301-302 阿多岡 貴様には無理 諦めろ 0304１３２人目の素数さん2021/02/27(土) 13:37:15.44ID:+FXN4YNO 阿多岡のニッポン自慢 キモイ 0305１３２人目の素数さん2021/02/27(土) 13:38:12.64ID:+FXN4YNO 人生の負け犬 阿多岡はガソリンかぶって焼身自殺な 🐖の丸焼きｗｗｗｗｗｗｗ 0306１３２人目の素数さん2021/02/27(土) 13:43:48.55ID:+FXN4YNO セカイ系 https://ja.wikipedia.org/wiki/%E3%82%BB%E3%82%AB%E3%82%A4%E7%B3%BB
銅 記事を真に受けてニッポン数学バンザイとわめく愛国馬鹿の阿多岡ｗ 0322１３２人目の素数さん2021/02/28(日) 07:44:47.62ID:ba03IeOv No State No Evil No Army No Murder No Money No Hunger 0323１３２人目の素数さん2021/02/28(日) 07:52:55.34ID:ba03IeOv 今年の目標 １．東京オリンピック開催阻止 ２．M子内親王の結婚の儀阻止
（参考） https://en.wikipedia.org/wiki/Modular_lambda_function Modular lambda function The relation to the j-invariant is[6][7] j(τ )= 256(1-λ (1-λ ))^3/{(λ (1-λ ))^2}= 256(1-λ +λ ^2)^3/{λ ^2(1-λ )^2} . which is the j-invariant of the elliptic curve of Legendre form y^2=x(x-1)(x-λ ) y^2=x(x-1)(x-λ )
https://www2.math.kyushu-u.ac.jp/~mkaneko/ https://www2.math.kyushu-u.ac.jp/~mkaneko/papers.html 金子昌信 論文 17. Supersingular j-invariants, hypergeometric series, and Atkin's orthogonal polynomials (with D. Zagier), AMS/IP Studies in Advanced Mathematics, vol. 7, 97--126, (1998). pdf https://www2.math.kyushu-u.ac.jp/~mkaneko/papers/atkin.pdf SUPERSINGULAR j-INVARIANTS, HYPERGEOMETRIC SERIES, AND ATKIN’S ORTHOGONAL POLYNOMIALS M. Kaneko and D. Zagier §1. Introduction. The polynomial describing supersingularity in terms of the λ-invariant of E (defined by writing E over K¯ in Legendre form y 2 = x(x - 1)(x - λ)) has a well-known and simple explicit expression, but a convenient expression for the polynomial expressing the condition of supersingularity directly in terms of the j-invariant (i.e., in terms of a Weierstrass model over K, without numbering the 2-torsion points over K¯ ) is less easy to find. In this (partially expository) paper, we will describe several different ways of constructing canonical polynomials in Q[j] whose reductions modulo p give ssp(j). 0326１３２人目の素数さん2021/02/28(日) 09:34:19.70ID:ba03IeOv>>324 >あんたは complete idiot ◆OHIXyLapqcだよね
（>>5） 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 p36 First, let us recall that if the once-punctured elliptic curve associated to EF fails to admit an F-core, (引用終り)
Analytic vs. algebraic This feature of Riemann surfaces allows one to study them with either the means of analytic or algebraic geometry. There is an equation
{\displaystyle [\wp '(z)]^{2}=4[\wp (z)]^{3}-g_{2}\wp (z)-g_{3},}{\displaystyle [\wp '(z)]^{2}=4[\wp (z)]^{3}-g_{2}\wp (z)-g_{3},} where the coefficients g2 and g3 depend on τ, thus giving an elliptic curve Eτ in the sense of algebraic geometry. Reversing this is accomplished by the j-invariant j(E), which can be used to determine τ and hence a torus.
Punctured spheres With three or more punctures, it is hyperbolic - compare pair of pants. 0333１３２人目の素数さん2021/02/28(日) 11:23:37.78ID:ba03IeOv>>331 正則行列も知らん落ちこぼれがいくらキーワードで検索しても 中身が読めないから無意味
