论文标题
从希尔伯特阶级领域的L功能中恢复代数曲线
Recovering algebraic curves from L-functions of Hilbert class fields
论文作者
论文摘要
在本文中，我们证明，可以从与曲线的Hilbert类阶层及其恒定场扩展相关的L功能中回收有限场上的平滑双曲线射击曲线。结果，我们给出了摩丘奇和塔玛川结果的新证明，即两种具有同构基本组的曲线本身就是同构。
In this paper, we prove that a smooth hyperbolic projective curve over a finite field can be recovered from L-functions associated to the Hilbert class field of the curve and its constant field extensions. As a consequence, we give a new proof of a result of Mochizuki and Tamagawa that two such curves with isomorphic fundamental groups are themselves isomorphic.
