论文标题
典型的brauer-manin障碍物在同质空间上具有强近似值
The étale Brauer-Manin obstruction to strong approximation on homogeneous spaces
论文作者
论文摘要
众所周知，在必要的非紧凑性假设下，brauer-manin障碍物是唯一在线性群体$ g $（或在连接的代数组下）在同质空间上进行强近似值的唯一一个，在适当的Tate-Shafarevich集团的有限性下，如果是$ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x $ x。在这项工作中，我们证明，在类似的假设下，对强近似值的典型brauer-manin障碍物是唯一具有任意稳定器的同质空间的障碍物。我们还处理了一些相关问题，涉及一组有限的估值之外的强近似值。最后，我们证明了一个兼容性结果，认为西里尔·德曼（Cyril Demarche）的工作是正确的，在商$ g/h $上的brauer-manin障碍物配对之间，其中$ g $和$ h $是连接的代数群，而$ h $是线性的，与这些空间相关的某些阿比亚化形态是线性的。
It is known that, under a necessary non-compactness assumption, the Brauer-Manin obstruction is the only one to strong approximation on homogeneous spaces $X$ under a linear group $G$ (or under a connected algebraic group, under assumption of finiteness of a suitable Tate-Shafarevich group), provided that the geometric stabilizers of $X$ are connected. In this work we prove, under similar assumptions, that the étale-Brauer-Manin obstruction to strong approximation is the only one for homogeneous spaces with arbitrary stabilisers. We also deal with some related questions, concerning strong approximation outside a finite set of valuations. Finally, we prove a compatibility result, suggested to be true by work of Cyril Demarche, between the Brauer-Manin obstruction pairing on quotients $G/H$, where $G$ and $H$ are connected algebraic groups and $H$ is linear, and certain abelianization morphisms associated with these spaces.
