nLab
inter-universal Teichmüller theory
Context
Arithmetic geometry
Contents
Idea
The generalization of Teichmüller theory to arithmetic geometry has been called inter-universal Teichmüller theory (often abbreviated IUTT ) by Shinichi Mochizuki .

The term “inter-universal” apparently refers to the fact that the theory is meant to formulated explicitly in a way that respects universe enlargement , hence that it is universe polymorphic (Mochizuki 12d, remark 3.1.4 , Yamashita 13 ).

It is claimed (Mochizuki 12d ) but currently unchecked that a proof of the abc conjecture can be found from anabelian geometry in this context.

References
Shinichi Mochizuki , Inter-universal Teichmüller theory I, Construction of Hodge theaters (2012) (pdf )

Shinichi Mochizuki , Inter-universal Teichmüller theory II, Hodge-Arakelov-theoretic evaluation (2012) (pdf )

Shinichi Mochizuki , Inter-universal Teichmüller theory III, Canonical splittings of the Log-theta-lattice (2012) (pdf )

Shinichi Mochizuki , Inter-universal Teichmüller theory IV, Log-volume computations and set-theoretic foundations (2012) (pdf )

Surveys include

Shinichi Mochizuki , Panoramic overview of inter-universal Teichmuller theory , pdf

Yamashita, FAQ on ‘Inter-Universality’ (pdf )

Ivan Fesenko , Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions , European Journal of Mathematics September 2015, Volume 1, Issue 3, pp 405-440 (publisher , pdf )

Minhyong Kim , Brief superficial remarks on Shinichi Mochizuki’s Interuniversal Teichmueller Theory (IUTT), version 1 , 10/11/2015, (pdf ).

Taylor Duypuy , Hodge Theaters: A First Look at the Big Hodge Theater , Confused Groups and Torsors

RIMS/Symmetries and Correspondences workshop : Inter-universal Teichmüller Theory Summit 2016

Jackson Morrow , Kummer classes and Anabelian geometry , notes from Super QVNTS : Kummer Classes and Anabelian Geometry 2017 (pdf )

Revised on February 23, 2017 11:27:39
by

Urs Schreiber
(147.231.89.7)