21/10/14 22:59:21.43 fCifkauW.net
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URLﾘﾝｸ(www.maths.nottingham.ac.uk)
News - Ivan Fesenko
Higher adelic theory, talk at Como school on Unifying Themes in Geometry, September 2021
URLﾘﾝｸ(www.maths.nottingham.ac.uk)
Higher adelic theory
Ivan Fesenko
Como School, September 27 2021
6 Anabelian geometry
P33
Anabelian geometry and IUT
Early work in anabelian geometry used CFT (or closely related theories) in
1D theory for global fields (Neukirch, Iwasawa, Ikeda, Uchida),
Neukirch’s CFT mechanism was influenced by his previous work in anabelian geometry.
Anabelian geometry for hyperbolic curves over number fields was proposed by Grothendieck and
pioneered by Nakamura, Tamagawa, Mochizuki.
Anabelian geometry includes
bi-anabelian geometry (restoring isomorphism classes of scheme theoretic objects) and
mono-anabelian geometry (restoring scheme theoretic objects).
These theories are group theoretical, algorithmic and explicit, features similarly to CFT
mechanism.
Powerful restoration results in absolute mono-anabelian geometry were established by Mochizuki
and applied in the IUT theory.
Watch Porowski’s talk for basic anabelian geometry.
Watch many talks of the 4 recent RIMS workshops on anabelian geometry and IUT
URLﾘﾝｸ(www.kurims.kyoto-u.ac.jp)
つづく