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

Fesenko, Ivan (2015) Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki. European Journal of Mathematics, 1 (3). pp. 405-440. ISSN 2199-675X

[img]
Preview
PDF - Requires a PDF viewer such as GSview, Xpdf or Adobe Acrobat Reader
Download (394kB) | Preview

Abstract

These notes survey the main ideas, concepts and objects of the work by Shinichi Mochizuki on interuniversal Teichmüller theory [31], which might also be called arithmetic deformation theory, and its application to diophantine geometry. They provide an external perspective which complements the review texts [32] and [33]. Some important developments which preceded [31] are presented in the first section. Several important aspects of arithmetic deformation theory are discussed in the second section. Its main theorem gives an inequality–bound on the size of volume deformation associated to a certain log-theta-lattice. The application to several fundamental conjectures in number theory follows from a further direct computation of the right hand side of the inequality. The third section considers additional related topics, including practical hints on how to study the theory.

Item Type: Article
Additional Information: The final publication is available at Springer via http://dx.doi.org/10.1007/s40879-015-0066-0
Keywords: Arithmetic, Geometry
Schools/Departments: University of Nottingham UK Campus > Faculty of Science > School of Mathematical Sciences
Identification Number: https://doi.org/10.1007/s40879-015-0066-0
Depositing User: Fesenko, Professor Ivan
Date Deposited: 07 Oct 2015 08:23
Last Modified: 14 Sep 2016 14:42
URI: http://eprints.nottingham.ac.uk/id/eprint/29224

Actions (Archive Staff Only)

Edit View Edit View