Algebra and geometry of arithmetic schemes

Lead Research Organisation: University of Nottingham
Department Name: Sch of Mathematical Sciences

Abstract

The cutting edge of modern number theory is the two-dimensional world of arithmetic surfaces such as a proper regular model of an elliptic curve over a global fields. Here geometry, algebra and arithmetic intertwine in a profound way. Recent advances in the area include the IUT theory of Shinichi Mochizuki and 2d adelic analysis and geometry of Ivan Fesenko. This work will look at further associated development in the area. The main focuse of this thesis is on fruitful interactions between algebraic and geometric aspects, towards new applications to solutions of fundamental problems.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N50970X/1 01/10/2016 30/09/2021
1946493 Studentship EP/N50970X/1 01/10/2017 30/09/2020 Christopher Hall