[過去ﾛｸﾞ] Inter-universal geometry と ABC予想 (応援スレ) 49 (1002ﾚｽ)
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479: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)11:04 ID:esT5rSCm(1/6)調 AAS
これ結構面白いので、メモ貼る
http://swc.math.arizona.edu/aws/1998/notes.html
The Southwest Center for Arithmetic Geometry
Arizona Winter School 1998
Course Descriptions and Notes
・ 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
480(5): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)11:23 ID:esT5rSCm(2/6)調 AAS
>>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.
481(3): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)11:26 ID:esT5rSCm(3/6)調 AAS
>>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. ”
この書き方だと、Mochizuki’s work は参考にしたが、直接は使っていないとあるね
だけど、これが本当の姿かもね
Mochizuki’s workを超えようとしている
482: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)11:32 ID:esT5rSCm(4/6)調 AAS
IUTの数学は着実に進みつつある
望月を認めつつも
それを乗り越え
前進している
483(1): 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)14:39 ID:esT5rSCm(5/6)調 AAS
無理矢理査読を通したとか
RIMSの陰謀だとか
そういう幼稚は議論は
アンチスレでやってくれ
現実に、IUTは数学界で着実に前進し
認められつつあるし
新しい成果も出ている
その例が、Kirti Joshi氏だよ (>>480-481)
484: 現代数学の系譜 雑談 ◆yH25M02vWFhP 2020/10/15(木)14:40 ID:esT5rSCm(6/6)調 AAS
>>483 タイポ訂正
そういう幼稚は議論は
↓
そういう幼稚な議論は
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