Joseph Gunther : Counting extensions of function fields geometrically

Posted by Nathan Jones , part of the Number Theory Seminar.

At

Oct. 18, 2016, 10 a.m.

In

SEO 427

Abstract

Recent work of Bhargava, Shankar, and Wang extended results on counting number fields of bounded discriminant and low degree over the rationals, to allow any global field as the base field. Their work uses geometry of numbers for both number fields and function fields. We'll explain how, in the function field case, one can instead give algebro-geometric proofs, which suggest new avenues for research and shed light on the geometry of the number field situation.