论文标题
某些品种的本地全球原则和整体泰特猜想
Local-global principle and integral Tate conjecture for certain varieties
论文作者
论文摘要
我们给出了一个几何标准，以检查平滑的投影型品种的一体式构想的有效性，该构想在编码率第一中与理性相关，并检查Brauer-manin障碍物是唯一的障碍物是唯一对局部全球原则对零循环的唯一构成零循环的原则，该零件是零循环的零分离型在全球范围内定义的，该领域是全球范围的。 我们证明，brauer-manin障碍物是在全球函数领域定义的所有几何理性表面上零循环的局部全球原理的唯一障碍，也是在奇数特征的全球函数字段中定义的第四个学位的del pezzo surfaces上的主体原理。 在此过程中，我们还证明了关于单周期在平滑的投射品种上的空间，该变化在Codimension One中与众不可地相连，这导致了Coniveau过滤的平等和强大的Coniveau过滤，以$ 3 $ $ 3 $的同源性。
We give a geometric criterion to check the validity of the integral Tate conjecture for one-cycles on a smooth projective variety that is separably rationally connected in codimension one, and to check that the Brauer-Manin obstruction is the only obstruction to the local-global principle for zero-cycles on a separably rationally connected variety defined over a global function field. We prove that the Brauer-Manin obstruction is the only obstruction to the local-global principle for zero-cycles on all geometrically rational surfaces defined over a global function field, and to the Hasse principle for rational points on del Pezzo surfaces of degree four defined over a global function field of odd characteristic. Along the way, we also prove some results about the space of one-cycles on a smooth projective variety that is separably rationally connected in codimension one, which leads to the equality of the coniveau filtration and the strong coniveau filtration on degree $3$ homology of such varieties.
