On rational points on classifying stacks and Malle's conjecture

2024/02/15 by Akhtari, Shabnam, Park, Jennifer, Pieropan, Marta +1
#11G50 #11R32 #11R45 #Algebraic Geometry (math.AG) #FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2402.10355

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(ℤ/nℤ) and Bμ_n.

Related

• Malle's conjecture and Brauer groups of stacks
• Heights on stacks and a generalized Batyrev-Manin-Malle conjecture
• The Batyrev-Manin conjecture for DM stacks
• Densities of rational points and number fields
• A counter example to Malle's conjecture on the asymptotics of discriminants