21/09/04 19:36:55.38 UOjWcMnu.net
凄いじゃないかIUT！ 「IUTは、類体論の拡張」
「フェセンコはIU幾何を遠アーベル幾何から派生した新たな類体論に位置付けている」
URLﾘﾝｸ(ja.wikipedia.org)
宇宙際タイヒミュラー理論
数論的 log Scheme 圏論的表示の構成等に続いた研究であり、「一点抜き楕円曲線付き数体」の「数論的タイヒミューラー変形」を遠アーベル幾何等を用いて「計算」する数論幾何学の理論である。イヴァン・フェセンコはIU幾何を遠アーベル幾何から派生した新たな類体論に位置付けている
URLﾘﾝｸ(www.maths.nottingham.ac.uk)
[R5] Class field theory, its three main generalisations, and applications pdf, May 2021, EMS Surveys 8(2021) 107-133
URLﾘﾝｸ(www.ems-ph.org)
EMS SURVEYS Vol8,2021 Class field theory, its three main generalisations, and applications
P16
Here are some relations between the three generalisations of CFT and their further developments:
2dLC?－－ 2dAAG－－－ IUT
l ／ ｜ ｜
l ／ ｜ ｜
l／ ｜ ｜
LC 2dCFT anabelian geometry
＼ ｜ ／
＼ ｜ ／
＼ ｜ ／
CFT
注）記号：
Class Field Theory (CFT), Langlands correspondences (LC), 2dAAG = 2d adelic analysis and geometry, two-dimensional (2d)
(P8 "These generalisations use fundamental groups: the etale fundamental group in anabelian geometry, representations of the etale fundamental group (thus, forgetting something very essential about the full fundamental group) in Langlands correspondences and the (abelian) motivic A1 fundamental group (i.e. Milnor K2) in two-dimensional (2d) higher class field theory.")
Problem 7. Find more direct relations between the generalisations of CFT. Use them to produce a single unified generalisation of CFT.23