Inverse Galois Problem and torsion points on abelian varieties

Lead Research Organisation: University of Bristol
Department Name: Mathematics

Abstract

One of the biggest unsolved questions in number theory is the Inverse Galois Problem. It is to show that every finite group can occur as a Galois group over the rationals. Abelian groups are well-understood through class field theory, and it is known (though it is very hard) that soluble groups can be realised as well. So a lot of work has been dedicated to simple and almost simple groups, and they can sometimes be realised from Galois groups of torsion points on curves and abelian varieties. This requires being able to construct curves that have some specific behaviour - automorphisms, endomorphisms, reduction types etc. Pip Goodman's research topic is to work in this direction, using recent developments in the theory of curves, their models, and their Jacobians.

Publications

10 25 50

Studentship Projects

Project Reference Relationship Related To Start End Student Name
EP/N509619/1 01/10/2016 30/09/2021
1940106 Studentship EP/N509619/1 18/09/2017 31/03/2021 Pip Goodman