On the p-adic variation of Heegner points
On the p-adic variation of Heegner points
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关于 Heegner 点的 p 进变分
DOI：
10.1017/s1474748019000094
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发表时间：
2019
影响因子：
0.9
通讯作者：
Castella, Francesc
中科院分区：
文献类型：
--
作者：
Castella, Francesc
本文证明了Hida家族中Bertolini-Darmon-Prasanna双变量级数与大Heegner点Howard系统有关的一个“显互反律”。作为应用，我们得到了经典Heegner环与大Heegner点的高权专化之间的直接关系，完善了作者早期的工作，并证明了在等变Birch猜想和Swinnerton-Dyer猜想预测的情况下，被二维Artin表示扭曲的CM椭圆曲线的Selmer群的消失。
In this paper, we prove an ‘explicit reciprocity law’ relating Howard’s system of big Heegner points to a two-variable -series of Bertolini–Darmon–Prasanna in Hida families. As applications, we obtain a direct relation between classical Heegner cycles and the higher weight specializations of big Heegner points, refining earlier work of the author, and prove the vanishing of Selmer groups of CM elliptic curves twisted by 2-dimensional Artin representations in cases predicted by the equivariant Birch and Swinnerton-Dyer conjecture.