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

Fesenko, Ivan

Authors

IVAN FESENKO ivan.fesenko@nottingham.ac.uk
Professor of Pure Mathematics



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.

Journal Article Type Article
Publication Date Aug 8, 2015
Journal European Journal of Mathematics
Electronic ISSN 2199-675X
Publisher Humana Press
Peer Reviewed Peer Reviewed
Volume 1
Issue 3
APA6 Citation Fesenko, I. (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), doi:10.1007/s40879-015-0066-0
DOI https://doi.org/10.1007/s40879-015-0066-0
Keywords Arithmetic, Geometry
Publisher URL http://link.springer.com/article/10.1007/s40879-015-0066-0
Copyright Statement Copyright information regarding this work can be found at the following address: http://eprints.nottingh.../end_user_agreement.pdf
Additional Information The final publication is available at Springer via http://dx.doi.org/10.1007/s40879-015-0066-0

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Copyright Statement
Copyright information regarding this work can be found at the following address: http://eprints.nottingham.ac.uk/end_user_agreement.pdf





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