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4: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [sage] 2020/06/20(土) 21:10:54.66 ID:OXXW5633

つづき

下記の PDF 数学の超難問「ABC予想」とは？
別冊Newton「数学の世界」 増補第3版 168 - 171 2019年11月 協力 小山信也 執筆 山田久美
これ分かり易いな
必見ですね（＾＾
https://researchmap.jp/koyama
researchmap 小山 信也 コヤマ シンヤ (Shin'ya Koyama)
https://researchmap.jp/koyama/avatar.JPG
https://researchmap.jp/koyama/misc/21300350/attachment_file.pdf
数学の超難問「ABC予想」とは？ 別冊Newton「数学の世界」 増補第3版 168 - 171 2019年11月 協力 小山信也 執筆 山田久美

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.
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:
P15
(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the diagram on §8.4 part 7, page 76 of the unpublished manuscript [Tan18] which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].
References
[SS17] Peter Scholze and Jakob Stix, Why abc is still a conjecture., 2017. 1, 1, 1e, 2, 7.5.3 ( http://www.kurims.kyoto-u.ac.jp/~motizuki/IUTch-discussions-2018-03.html )
[Tan18] Fucheng Tan, Note on IUT, 2018. 1, 2
つづく

http://rio2016.5ch.net/test/read.cgi/math/1592654877/4

51: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/06/27(土) 23:01:24.66 ID:jEjJjPRO

”Teichmuller space” 良く纏まっている
https://en.wikipedia.org/wiki/Teichm%C3%BCller_space
Teichmuller space

The geometric vein in the study of Teichmuller space was revived following the work of William Thurston in the late seventies, who introduced a geometric compactification which he used in his study of the mapping class group of a surface.
Other more combinatorial objects associated to this group (in particular the curve complex) have also been related to Teichmuller space, and this is a very active subject of research in geometric group theory.

Quadratic differentials and the Bers embedding
Main article: Schwarzian derivative
Main article: Bers slice

https://upload.wikimedia.org/wikipedia/commons/thumb/7/71/Bers-Einbettung.png/220px-Bers-Einbettung.png
Image of the Bers embedding of a punctured torus' 2-dimensional Teichmuller space

https://en.wikipedia.org/wiki/Moduli_of_algebraic_curves
Moduli of algebraic curves

つづく

http://rio2016.5ch.net/test/read.cgi/math/1592654877/51

180: 現代数学の系譜 雑談 ◆yH25M02vWFhP  [] 2020/07/19(日) 09:47:59.66 ID:2Y0qBKwb

>>179
つづき

; later he has refined this result and shown that K may be recovered from the topological group GK and one Lubin-Tate character of GK (see [14] and [20]).

On the other hand, given a padic field K1, the Jarden-Ritter Theorem (see [8]) provides a characterization of all p-adic fields
K2 such that one has a topological isomorphism GK2 ' GK1 of their absolute Galois groups and
it is well-known that for every prime p, pairs of fields with this property always exists.
Mochizuki’s anabelian reconstruction yoga (see [22] and its references) provides, starting with
the topological group G ' GK, the reconstruction amphora of G (see [6, 5, 7, 20, 21, 22] and
its references for the contents of the reconstruction amphora; in [9] I introduced this term as a
convenient short-form and memory-aid) which contains all quantities related to K which are reconstructed from the topological group G such as the prime p,
the topological monoids O^*K (the group of units of the ring of integers OK of K) and OΔK the multiplicative monoid of non-zero elements of OK (this notation is due to Mochizuki).

However the ring OK is not contained in the reconstruction amphora of G.
Moreover Mochizuki’s Reconstruction yoga also asserts that if one has an isomorphism of
topological groups
GK1 〜＝ GK2
then an isomorphism of the topological monoids
OΔK1 〜＝ OΔK2
may also be reconstructed from it (see [6, Section 2]).

つづく

http://rio2016.5ch.net/test/read.cgi/math/1592654877/180

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