AI 中文总结
本文针对数域上的商叠，推广了簇的局部-整体障碍关系，证明Étale-Brauer障碍是多种相关障碍中最精细的一种，拓展了代数叠上局部-整体障碍的研究。
AI 中文摘要
对于数域k上的商叠[X/G]，其中X是光滑拟射影几何整k簇，G是线性k群，我们推广了簇上局部-整体障碍间的若干关系，证明了Étale-Brauer障碍是迭代下降、有限下降、下降、Brauer-Manin等各类障碍中最精细的一种。
英文摘要
Let k be a number field. For quotient stacks [X/G] with X a smooth quasi-projective geometrically integral k-variety and G a linear k-group, we extend several relations between local-global obstructions previously known for varieties, showing that étale-Brauer obstruction is the finest among various obstructions (such as iterated descent, finite descent, descent, Brauer-Manin).
CommentsSection 3 was rewritten with new lemmas fixing geometric-integrality plus typo/layout polish. 18 pages, git commit 81c812
