On rational points on classifying stacks and Malle's conjecture

Abstract

In this expository article, we compare Malle's conjecture on counting number fields of bounded discriminant with recent conjectures of Ellenberg--Satriano--Zureick-Brown and Darda--Yasuda on counting points of bounded height on classifying stacks. We illustrate the comparisons via the classifying stacks $B(\mathbb{Z}/n\mathbb{Z})$ and $B{\mu_n}$.