Inter-universal geometry と ABC予想 (応援スレ) 49

Inter-universal geom ..

531:現代数学の系譜雑談
20/10/18 10:47:20.84 ZLSkSSTT.net
メモ貼る。下記、Fig. 1 PDF中に図があるけど、IUT読む人は頭に入れておくのが良いと思う（＾＾
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)
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.
Fig. 1. IUT, Topics & References as potential entry points.
● Diophantine: Heights, Faltings’ isogenies & Abc.
● Anabelian: Mono-anabelian reconstruction & Tripodal transports.
● Geometry: Multiradiality, Coricity & Arithmetic Analyticity vs Holomorphicity.
● Categorical: Frobenioids, Anabelioid, Prime Strips & Hodge Theaters.
● Meta-Abelian Theta: Mumford’s abelian constructions & Kummer theory.
つづく

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