Arithmetic Geometry and Number Theory RTG Seminar: Distributions of unramified extensions of global fields

Seminar | September 16 | 3:10-5 p.m. | 740 Evans Hall | Note change in location

 Melanie Matchett Wood, UC Berkeley

 Department of Mathematics

We give conjectures on the distribution of the Galois groups of the maximal unramified extensions of Galois Γ-number fields or function fields for any finite group Γ (for the part of the Galois group prime to the order of Γ and the order of roots of unity in the base field). We explain some results about these Galois groups that motivate us to build certain random groups whose distributions appear in our conjectures. We give theorems in the function field case (as the size of the finite field goes to infinity) that support these new conjectures. In particular, our distributions abelianize to the Cohen-Lenstra-Martinet distributions for class groups, and so our function field theorems give support to (suitably modified) versions of the Cohen-Lenstra-Martinet heuristics. This talk is on joint work with Yuan Liu and David Zureick-Brown.