Algebraic Tori and a Computational Inverse Galois Problem

Algebraic tori play a central role in the structure theory and representation theory of algebraic groups. I will describe an ongoing project to investigate algebraic tori over p-adic fields. The project naturally divides into two parts: finding finite subgroups of $GL(n,\mathbb{Z})$ and listing all p-adic fields with a given Galois group. I will summarize existing work on the first part, and present a new algorithm for the second problem. I will include an introduction to algebraic tori, p-adic fields and local class field theory for members of the audience who have not studied these topics or need a refresher.

The speaker is a candidate for a position in the Department.