Abstract or Additional Information
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,Z) and listing all p-adic fields with a given Galois group. I will describe existing work that computes these subgroups for small n, and an algorithm for finding p-adic fields with a given Galois group. In addition, I will give an indication of how feasible the problem of listing all p-adic fields with a given Galois group is by bounding the number of such fields.
This talk will overlap with a colloquium that I gave here at Pitt in January, but there are new results to report.