On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves
On the non-triviality of the $p$-adic Abel–Jacobi image of generalised Heegner cycles modulo $p$, I: Modular curves
复制标题
关于广义 Heegner 循环模 $p$ 的 $p$-adic Abel-Jacobi 图像的非平凡性，I：模曲线
DOI：
10.1090/jag/748
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发表时间：
2014
影响因子：
1.8
通讯作者：
Ashay A. Burungale
中科院分区：
文献类型：
--
作者：
Ashay A. Burungale
.广义Heegner圈与虚二次扩张K/ Q上的一对椭圆新形和一个Hecke特征标相关联。设p是K/ Q中可分裂的奇素数，且n = 6 = p是奇无分支的艾德素数.本文证明了K的Z-反分元扩张上模p的广义Heegner圈的p -进Abel-Jacobi象的非平凡性。这个结果是改进的Bloch-Beilinson猜想和Bloch-Kato猜想的一个证据。在权为2且K是一个普通素数的情况下，它提供了Cornut和Vatsal关于Mazur猜想的结果的一个非平凡的改进，该猜想关于K的Z-反分元扩张上的Heegner点的非平凡性。在重量为2和超奇异素数的情况下，它解决了Mazur猜想早期已知的只是对于超奇异素数。
. Generalised Heegner cycles are associated with a pair of an elliptic newform and a Hecke character over an imaginary quadratic extension K/ Q . Let p be an odd prime split in K/ Q and ℓ 6 = p an odd unramified prime. We prove the non-triviality of the p -adic Abel–Jacobi image of generalised Heegner cycles modulo p over the Z ℓ -anticylotomic extension of K . The result is an evidence for the refined Bloch–Beilinson and the Bloch–Kato conjecture. In the case of weight two and ℓ an ordinary prime, it provides a non-trivial refinement of the results of Cornut and Vatsal on Mazur’s conjecture regarding the non-triviality of Heegner points over the Z ℓ -anticylotomic extension of K . In the case of weight two and ℓ a supersingular prime, it settles Mazur’s conjecture earlier known just for ℓ ordinary.