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Malle's conjecture and Brauer groups of stacks

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arxiv 2412.04196 v3 pith:AXH3P3AC submitted 2024-12-05 math.NT math.AG

Malle's conjecture and Brauer groups of stacks

Daniel Loughran , Tim Santens This is my paper
classification math.NT math.AG
keywords conjecturebrauerboundedgroupsmallestacksalgebraicbatyrev-manin
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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.

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