论文标题
0季的下降和埃塔尔武器障碍物
Descent and étale-Brauer obstructions for 0-cycles
论文作者
论文摘要
对于在数字字段上的多种情况下的0循环，我们定义了用于理性点的经典下降集的类似物。除其他外，这导致了0个周期的典型brauer障碍物的定义，我们显示的这包含在Brauer-Manin集合中，并且与Suslin的学位0的单数同源性兼容。然后，我们将一些工具和技术转移到研究设置中的一些工具和技术。例如，我们将Y. Liang制定的策略扩展到将基本场上有限扩展的理性点的算术与0循环的有限扩展相关的，并将其与Torsors相关。我们提供了结果的应用，以研究0循环的算术行为，以供应表面，（扭曲的）Kummer品种，通用Torsors和Torsors在Tori下给出。
For 0-cycles on a variety over a number field, we define an analogue of the classical descent set for rational points. This leads to, among other things, a definition of the étale-Brauer obstruction set for 0-cycles, which we show is contained in the Brauer-Manin set and is compatible with Suslin's singular homology of degree 0. We then transfer some tools and techniques used to study the arithmetic of rational points into the setting of 0-cycles. For example, we extend the strategy developed by Y. Liang, relating the arithmetic of rational points over finite extensions of the base field to that of 0-cycles, to torsors. We give applications of our results to study the arithmetic behaviour of 0-cycles for Enriques surfaces, torsors given by (twisted) Kummer varieties, universal torsors, and torsors under tori.
