ガロア第一論文と乗数イデアル他関連資料スレ2

[過去ﾛｸﾞ] ガロア第一論文と乗数イデアル他関連資料スレ2 (1002ﾚｽ)
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12(3): １３２人目の素数さん [] 2023/03/04(土)13:14 ID:Ykziy9We(5/7)
>>10

"Kohn" Multiplier ideal
で検索すると下記ヒット
起源は、ここの[ 8] J. J. Kohn,(1979)かな
下記”microlocal”は、佐藤の”microlocal”か？
・・そうみたい、はっきり分からないがｗ

https://projecteuclid.org/proceedings/advanced-studies-in-pure-mathematics/complex-analysis-in-several-variables-memorial-conference-of-kiyoshi-oka/Chapter/Ideals-of-multipliers/10.2969/aspm/04210147
VOL. 42 | 2004
Ideals of multipliers
Joseph J. Kohn
Adv. Stud. Pure Math., 2004: 147-157 (2004)
https://projecteuclid.org/ebooks/advanced-studies-in-pure-mathematics/Complex-Analysis-in-Several-Variables--Memorial-Conference-of-Kiyoshi/chapter/Ideals-of-multipliers/10.2969/aspm/04210147.pdf

Ideals of multipliers were introduced in [8] to find conditions on domains in complex manifolds under which subellipticity of the ∂ -Neumann problem holds.
Similar ideals were used to study subellipticity on of □b on CR manifolds (see [9] ).

つづく

13: １３２人目の素数さん [] 2023/03/04(土)13:14 ID:Ykziy9We(6/7)
>>12
つづき

Ideals of holomorphic multipliers in a somewhat different context have been
used by Nadel (see [15]) and by Siu (see [16]) to prove global theorems
in algebraic geometry. Here we will be concerned with the ideals that
arise in the study of local regularity. We will briefly explain the use
of subelliptic estimates then we define local and microlocal multipliers
and show how to use them to derive subelliptic estimates. We also discuss the use of subelliptic multipliers when subellipticity fails. Finally we show how subelliptic multipliers give rise to invariants of complex
analytic varieties.

[ 8] J. J. Kohn, Subellipticity of the ∂^- -Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979), 79-122. https://projecteuclid.org/journals/acta-mathematica/volume-142/issue-none/Subellipticity-of-the-bar-partial--Neumann-problem-on-pseudo/10.1007/BF02395058.full
[ 9] J. J. Kohn, Microlocalization of CR structures, Proceedings Several Complex Variables, Hangzhou Conference 1981, Birkhauser, Boston 1984,
29-36,.
(引用終り)

追加
>[ 8] J. J. Kohn, Subellipticity of the ∂^- -Neumann problem on pseudoconvex domains: sufficient conditions, Acta Math. 142 (1979)
・”§1. Introduction The main idea of this work is to analyze a-priori estimates for partial differential operators using the theory of ideals of functions.”
最初の[ 8]では、用語”Multiplier ideal”は、不使用みたい
以上

18(1): １３２人目の素数さん [] 2023/03/04(土)19:00 ID:JhTBBGo5(2/2)
>>12
>>下記”microlocal”は、佐藤の”microlocal”か？

溝畑のmicrolacalでもある。

Microlocal analysis considers (generalized, hyper-) functions, operators, etc. in the "microlocal" range. Here, "microlocal" means seeing the matter more locally than usual by introducing the (cotangential) direction at every point. In Fourier analysis it corresponds to viewing things locally in both x
and ξ
. In view of the uncertainty principle, this is possible only by considering the objects modulo regular parts. This idea was first used in the study of pseudo-differential operators by P.D. Lax, S. Mizohata, L. Hörmander, etc. V.P. Maslov has enriched the theory by the introduction of a canonical structure. M. Sato has constructed the sheaf of micro-functions on the cotangent sphere bundle S∗M
of the base space M
as the basic object of microlocal analysis.

384: １３２人目の素数さん [] 2023/03/14(火)20:52 ID:5bTCTU61(4/7)
>>380
ありがとう
なるほど
それは一つの見解ではあるね

で、正しいかどうか分からないが
Inter-universal geometry と ABC予想 (応援スレ) 68
2chｽﾚ:math
281 2023/03/14(火) 02:38:22.45 ID:EzJL6k5J
>>12
Joshi は自分の論文のパートIIIでABC予想解けるって言ってたけど
先だって出したのはパートIIの書き直しだな早よしろ
ショルツェは女子と話してて自分が文句があるのは望月の書き方みたいな事言ってたみたいだし
早よ決着つけて
(引用終り)

これ下記かな？　JoshiのパートIIIでABC予想解けて、認められたら
IUTにも春が来るかな？ｗ

https://arxiv.org/abs/2303.01662
[Submitted on 3 Mar 2023]
Construction of Arithmetic Teichmuller spaces II: Proof of a local prototype of Mochizuki's Corollary~3.12
Kirti Joshi
This paper deals with consequences of the existence of Arithmetic Teichmuller spaces established arXiv:2106.11452 and arXiv:2010.05748. Theorem~9.2.1 provides a proof of a local version of Mochizuki's Corollary~3.12. Local means for a fixed p-adic field. There are several new innovations in this paper. Some of the main results are as follows. Theorem~3.5.1 shows that one can view the Tate parameter of Tate elliptic curve as a function on the arithmetic Teichmuller space of [Joshi, 2021a], [Joshi, 2022b]. The next important point is the construction of Mochizuki's Θgau-links and the set of such links, called Mochizuki's Ansatz in \S6. Theorem~6.9.1 establishes valuation scaling property satisfied by points of Mochizuki's Ansatz (i.e. by my version of Θgau-links). These results lead to the construction of a theta-values set (\S8) which is similar to Mochizuki's Theta-values set (differences between the two are in \S8.7.1). Finally Theorem~9.2.1 is established. For completeness, I provide an intrinsic proof of the existence of Mochizuki's log-links (Theorem 10.9.1), log-links (Theorem~10.14.1) and Mochizuki's log-Kummer Indeterminacy (Theorem~10.19.1) in my theory.

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