论文标题
高级共同学中的Waldspurger公式
Waldspurger formulas in higher cohomology
论文作者
论文摘要
经典的Waldspurger公式计算最大圆环的四元素自动形式的时期，已用于多种算术应用中，例如在等级0情况下的Birch和Swinnerton-Dyer猜想。这就是为什么该公式被认为是著名的Gross-Zagier公式的等级0类似物的原因。 另一方面，Eichler-Shimura的对应关系使我们能够将这种Quaternionic自增生形式解释为某些算术群的较高共同体学空间中的共生。通过这种方式，我们可以实现某些Shimura品种的依托共同体中相应的自动形式。在这项工作中，我们发现了一个类似于Waldspurger的公式，该公式与该cocycle和最大圆环相关的基本类别的帽子产物与Rankin-Selberg L-功能的特殊值相关。
The classical Waldspurger formula, which computes periods of quaternionic automorphic forms in maximal torus, has been used in a wide variety of arithmetic applications, such as the Birch and Swinnerton-Dyer conjecture in rank 0 situations. This is why this formula is considered the rank 0 analogue of the celebrated Gross-Zagier formula. On the other hand, Eichler-Shimura correspondence allows us to interpret this quaternionic automorphic form as a cocycle in higher cohomology spaces of certain arithmetic groups. In this way we can realize the corresponding automorphic representation in the etale cohomology of certain Shimura varieties. In this work we find a formula, analogous to that of Waldspurger, which relates cap-products of this cocycle and fundamental classes associated with maximal torus with special values of Rankin-Selberg L-functions.
