Malle's conjecture and Brauer groups of stacks
Number Theory
2025-06-25 v3 Algebraic Geometry
Abstract
We put forward a conjecture for the leading constant in Malle's conjecture on number fields of bounded discriminant, guided by stacky versions of conjectures of Batyrev-Manin, Batyrev-Tschinkel, and Peyre on rational points of bounded height on Fano varieties. A new framework for Brauer groups of stacks plays a key role in our conjecture, and we define a new notion of the unramified Brauer group of an algebraic stack.
Cite
@article{arxiv.2412.04196,
title = {Malle's conjecture and Brauer groups of stacks},
author = {Daniel Loughran and Tim Santens},
journal= {arXiv preprint arXiv:2412.04196},
year = {2025}
}
Comments
110 pages. Comments welcome. Revised intro (Section 1.4) to make main theorems more clear