Malle's conjecture and Brauer groups of stacks

Daniel Loughran; Tim Santens

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arXiv · 2412.04196

Malle's conjecture and Brauer groups of stacks

Daniel Loughran·Tim Santens

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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.

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Daniel Loughran, Tim Santens. 2024-12-05. Malle's conjecture and Brauer groups of stacks. https://arxiv.org/abs/2412.04196

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