AI 中文总结
该研究在具有拟射粗模空间的有限型光滑分离德利涅-芒福德堆叠上，证明下降障碍包含于布饶尔-马林障碍，且下降障碍与 étale 布饶尔-马林障碍、迭代下降障碍一致，布饶尔-马林障碍也与迭代布饶尔-马林障碍一致。
AI 中文摘要
我们推广并比较了数域上代数堆叠的局部-整体障碍。对于具有拟射粗模空间的有限型光滑分离德利涅-芒福德堆叠，我们证明下降障碍包含在布饶尔-马林障碍中。通过提升$\boldsymbol{\text{G}_m}$-挠子，我们得到对应复合障碍间的包含关系。我们还证明，在该设定下，下降障碍与 étale 布饶尔-马林障碍、迭代下降障碍均一致，且布饶尔-马林障碍也与迭代布饶尔-马林障碍一致。
英文摘要
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 étale Brauer-Manin obstruction and the iterated descent obstruction. The Brauer-Manin obstruction also coincides with the iterated Brauer-Manin obstruction.
Comments39 pages
