论文标题
有效妨碍从积极特征提升泰特班级
Effective obstruction to lifting Tate classes from positive characteristic
论文作者
论文摘要
我们给出了一种在数字字段上采用平滑性的算法，并计算有限降低的泰特类别的阻塞图的$ p $ - ad近似。这给出了高空表面的“中间PICARD号”上的上限。对现有方法的改进是，我们的方法仅依赖于单个质量降低，并有可能将泰特类的维度减少两个或更多。阻塞图来自$ p $ - ad的变异性霍奇猜想，我们依靠Bloch-Esnault-Kerz最近的进步来解释我们的界限。
We give an algorithm that takes a smooth hypersurface over a number field and computes a $p$-adic approximation of the obstruction map on the Tate classes of a finite reduction. This gives an upper bound on the "middle Picard number" of the hypersurface. The improvement over existing methods is that our method relies only on a single prime reduction and gives the possibility of cutting down on the dimension of Tate classes by two or more. The obstruction map comes from $p$-adic variational Hodge conjecture and we rely on the recent advancement by Bloch-Esnault-Kerz to interpret our bounds.
