论文标题
在Quaternionic环境中
Generalized Heegner cycles and $p$-adic $L$-functions in a quaternionic setting
论文作者
论文摘要
在最近的一篇论文中，Castella和Hsieh证明了与与假想二次领域的Hecke角色相关的Galois表示相关的Selmer群体的结果。这些结果是在所谓的Heegner假设下获得的，即假想的二次场相对于模块化形式的水平满足。特别是，Castella和Hsieh证明了Bloch-kato猜想的排名0案例，以$ l $ undions在其环境中的模块化形式。 Castella和Hsieh工作的关键是广义Heegner Cycles与$ P $ -ADIC $ L $ functions之间的显着联系。在本文中，Castella-hsieh的几个结果扩展到了Quaternionic设置，即当一个人以“放松”的Heegner假设下工作时会产生的设置。更明确地，我们证明了Selmer组的消失和一维结果。我们策略中的关键成分是布鲁克斯在Shimura曲线上广泛的Heegner周期的结果。
In a recent paper, Castella and Hsieh proved results for Selmer groups associated with Galois representations attached to newforms twisted by Hecke characters of an imaginary quadratic field. These results are obtained under the so-called Heegner hypothesis that the imaginary quadratic field satisfies with respect to the level of the modular form. In particular, Castella and Hsieh prove the rank 0 case of the Bloch-Kato conjecture for $L$-functions of modular forms in their setting. The key point of the work of Castella and Hsieh is a remarkable link between generalized Heegner cycles and $p$-adic $L$-functions. In this paper, several of the results of Castella-Hsieh are extended to a quaternionic setting, that is, the setting that arises when one works under a "relaxed" Heegner hypothesis. More explicitly, we prove vanishing and one-dimensionality results for Selmer groups. Crucial ingredients in our strategy are Brooks's results on generalized Heegner cycles over Shimura curves.
