论文标题
振动方法将零循环的应用在某些品种上存在于Brauer-Manin障碍物上的零循环中的存在
Applications of the fibration method for zero-cycles to the Brauer-Manin obstruction to the existence of zero-cycles on certain varieties
论文作者
论文摘要
我们研究了Brauer-manin障碍物，以在数量字段上某些类别的品种中存在零循环$ d $的零循环。我们将现有的结果推广到文献中，并证明了有关纤维上纤维的一些结果，在该线路上，通用纤维的几何brauer组不假定为有限。这个想法是假设对哈斯原理的brauer-manin障碍物是某些纤维的唯一一个，然后推断出零循环的类似结果。
We study the Brauer-Manin obstruction to the existence of zero-cycles of degree $d$ on certain classes of varieties over number fields. We generalise existing results in the literature and prove some results about fibrations over the projective line, where the geometric Brauer group of the generic fibre is not assumed to be finite. The idea is to assume that the Brauer-Manin obstruction to the Hasse principle is the only one for certain fibres and then deduce analogous results for zero-cycles.
