Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta-functions, notes on the work of Shinichi Mochizuki

Ivan Fesenko
2015 European Journal of Mathematics  
Fesenko is an introduction to inter-universal Teichmüller theory, as developed by Shinichi Mochizuki, and its application to famous conjectures in Diophantine geometry. In a series of preprints released several years ago, Mochizuki introduced a vast collection of new ideas and methods related to arithmetic deformation. The level of novelty of the theory has made it challenging to study even for many experts in arithmetic geometry. The article surveys the main features and objects of the work of
more » ... Mochizuki and also provides an independent perspective. We hope that the article will be of help in understanding the main concepts and innovations of this important theory. Abstract These notes survey the main ideas, concepts and objects of the work by Shinichi Mochizuki on inter-universal Teichmüller theory (Inter-universal Teichmüller theory I-IV, 2012-2015) which might also be called arithmetic deformation theory, and its application to diophantine geometry. They provide an external perspective which complements the review texts of Mochizuki (Invitation to inter-universal Teichmüller theory (lecture note version), 2015) and (Algebraic Number Theory and
doi:10.1007/s40879-015-0066-0 fatcat:xrpw4vw74jd5ved7srzh3jnksy