论文标题
贝林森几何高度配对的概括
A generalization of Beilinson's geometric height pairing
论文作者
论文摘要
在他关于高度配对的开创性论文的第一部分中，贝林森构建了一个$ \ ell $ - ad的高度配对，用于在平稳曲线上的平滑曲线磁场上的互补编成互补的互补编成的合理杂志循环，并询问了代数封闭的场上的曲线，并询问通用较高的上限基底。在本文中，我们通过构建在代数封闭的平滑品种$ b $上定义的品种的配对来回答贝林森的问题，而在第二$ \ ell $ - $ - 亚种共同体$ b $中，值为$ b $。超过$ \ bbb c $我们的配对实际上是$ \ bbb q $值，总的来说，我们推测其几何来源。
In the first section of his seminal paper on height pairings, Beilinson constructed an $\ell$-adic height pairing for rational Chow groups of homologically trivial cycles of complementary codimension on smooth projective varieties over the function field of a curve over an algebraically closed field, and asked about an generalization to higher dimensional bases. In this paper we answer Beilinson's question by constructing a pairing for varieties defined over the function field of a smooth variety $B$ over an algebraically closed field, with values in the second $\ell$-adic cohomology group of $B$. Over $\Bbb C$ our pairing is in fact $\Bbb Q$-valued, and in general we speculate about its geometric origin.
