Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki
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 revi...
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| Format: | Article |
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Springer
2015
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| Online Access: | https://eprints.nottingham.ac.uk/29224/ |
| _version_ | 1848793741787136000 |
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| author | Fesenko, Ivan |
| author_facet | Fesenko, Ivan |
| author_sort | Fesenko, Ivan |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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. |
| first_indexed | 2025-11-14T19:05:07Z |
| format | Article |
| id | nottingham-29224 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:05:07Z |
| publishDate | 2015 |
| publisher | Springer |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-292242020-05-04T17:15:27Z https://eprints.nottingham.ac.uk/29224/ Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki Fesenko, Ivan 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. Springer 2015-08-08 Article PeerReviewed 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 Arithmetic Geometry http://link.springer.com/article/10.1007/s40879-015-0066-0 doi:10.1007/s40879-015-0066-0 doi:10.1007/s40879-015-0066-0 |
| spellingShingle | Arithmetic Geometry Fesenko, Ivan Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title | Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title_full | Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title_fullStr | Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title_full_unstemmed | Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title_short | Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki |
| title_sort | arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of shinichi mochizuki |
| topic | Arithmetic Geometry |
| url | https://eprints.nottingham.ac.uk/29224/ https://eprints.nottingham.ac.uk/29224/ https://eprints.nottingham.ac.uk/29224/ |