论文标题
RSZ单一shimura曲线的算术gan-gross-prasad猜想
Arithmetic Gan-Gross-Prasad conjecture for RSZ unitary Shimura curves
论文作者
论文摘要
XUE通过Quaternionic shimura曲线的算术gan-gross-prosaD猜想的算术gan-gross-prosad猜想的统一shimura曲线曲线证明了方程性的细化。另一方面，Rapoport，Smithling和Zhang使用改良的Pel型Shimura品种提出了猜想的变体，我们称之为RSZ Shimura品种。我们根据修改后的Shimura曲线重新解释了XUE的结果。然后，我们使用重新解释来证明猜想的变体的情况。我们的结果与XUE的工作相结合，建立了变体和毛质子公式之间的联系。
Xue proved an equational refinement of the unitary Shimura curve case of the arithmetic Gan-Gross-Prasad conjecture via the Gross-Zagier formula for quaternionic Shimura curves. On the other hand, Rapoport, Smithling and Zhang posed a variant of the conjecture, using modified PEL type Shimura varieties, which we call RSZ Shimura varieties. We reinterpret the result of Xue in terms of the modified Shimura curves. We then use the reinterpretation to prove a case of the variant of the conjecture. Our result combined with the work of Xue establishes a connection between the variant and the Gross-Zagier formula.
