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Generalised Kawada-Satake method for Mackey functors in class field theory (2018)
Journal Article
Fesenko, I., Vostokov, S. V., & Yoon, S. H. (2018). Generalised Kawada-Satake method for Mackey functors in class field theory. European Journal of Mathematics, 4(3), 953–987. doi:10.1007/s40879-018-0245-x

We propose and study a generalised Kawada--Satake method for Mackey functors in the class field theory of positive characteristic. The root of this method is in the use of explicit pairings, such as the Artin--Schreier--Witt pairing, for groups desc... Read More

Arithmetic deformation theory via arithmetic fundamental groups and nonarchimedean theta functions, notes on the work of Shinichi Mochizuki (2015)
Journal Article
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. ISSN 2199-675X

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... Read More