论文标题
Quaternionic Shimura曲线的模块化高度
Modular Heights of Quaternionic Shimura Curves
论文作者
论文摘要
本文的目的是证明一个公式，表达Quaternionic Shimura曲线的模块化高度，就完全真实数字字段的Dedekind Zeta函数的对数衍生物而言，完全真实的数字字段上。我们的证明是基于Yuan-Zhang-Zhang对总体公式的工作以及Yuan-Zhang在平均Colmez猜想上的工作。所有这些作品反过来又受到了Gross-Zagier的开拓性工作和Kudla计划的一些哲学的启发。
The goal of this paper is to prove a formula expressing the modular height of a quaternionic Shimura curve over a totally real number field in terms of the logarithmic derivative of the Dedekind zeta function of the totally real number field. Our proof is based on the work of Yuan-Zhang-Zhang on the Gross-Zagier formula and the work of Yuan-Zhang on the averaged Colmez conjecture. All these works are in turn inspired by the Pioneering work of Gross-Zagier and some philosophies of Kudla's program.
