论文标题
通过霍奇结构的限制计算高度
Computing heights via limits of Hodge structures
论文作者
论文摘要
我们考虑了明确计算贝林森（Beilinson）的问题 - 在数字字段上定义的品种上的同源性周期的bloch高度。最近的结果已经建立了一个一致性，直到素数的对数的合理跨度，一定极限混合霍奇结构的高度与某些贝林森（Beilinson） - 从带有节点的奇数高度丘角获得的beilinson- bloch高度。这种一致性提出了一种计算贝林森 - 布洛克高度的新方法。在这里，我们解释了如何在实践中计算相关极限混合Hodge结构，然后将我们的计算方法应用于节点四分之一的曲线和淋巴结三次三倍。在这两种情况下，我们都会解释一致性中发生的素数的性质。
We consider the problem of explicitly computing Beilinson--Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes, between the height of certain limit mixed Hodge structures and certain Beilinson--Bloch heights obtained from odd-dimensional hypersurfaces with a node. This congruence suggests a new method to compute Beilinson--Bloch heights. Here we explain how to compute the relevant limit mixed Hodge structures in practice, then apply our computational method to a nodal quartic curve and a nodal cubic threefold. In both cases, we explain the nature of the primes occurring in the congruence.
