Descent and Brauer-Manin Obstructions on Deligne-Mumford Stacks

Donghao Li; Sheng Liu; Chang Lv; Chen Zhang

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arXiv · 2608.24649

Descent and Brauer-Manin Obstructions on Deligne-Mumford Stacks

Donghao Li·Sheng Liu·Chang Lv·Chen Zhang

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Abstract

We generalize and compare local-global obstructions for algebraic stacks over number fields. For smooth separated Deligne-Mumford stacks of finite type with a quasi-projective coarse moduli space, we prove that the descent obstruction is contained in the Brauer--Manin obstruction. By lifting $\mathbb{G}_m$-gerbes, we obtain an inclusion between the corresponding composite obstructions. We also show that in this setting the descent obstruction coincides with both the \'etale Brauer-Manin obstruction and the iterated descent obstruction. The Brauer-Manin obstruction also coincides with the iterated Brauer-Manin obstruction.

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BibTeX RIS

Donghao Li, Sheng Liu, Chang Lv, Chen Zhang. 2026-08-25. Descent and Brauer-Manin Obstructions on Deligne-Mumford Stacks. https://arxiv.org/abs/2608.24649

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