Zero Cycles on a Product of Elliptic Curves Over a p -adic Field
Zero Cycles on a Product of Elliptic Curves Over a p -adic Field
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p 进场上椭圆曲线乘积的零循环
DOI：
10.1093/imrn/rnab020
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发表时间：
2021
影响因子：
1
通讯作者：
Leal, Isabel
中科院分区：
文献类型：
--
作者：
Gazaki, Evangelia;Leal, Isabel
本文考虑了在有限扩张上的椭圆曲线的乘积，它具有良好的或分裂的乘法约化的组合。我们假设至多有一条椭圆曲线具有超奇异约化。在这些假设下，我们证明了Albanese内核的是一个有限群和一个可分群的直接和，扩展工作的Raskind和Spiess的情况下，包括超奇异现象。我们的方法包括研究循环映射的核。我们给出了具体的标准，保证这个地图是单射的。当所有的曲线有良好的普通减少，我们表明，它足以扩展到一个特定的有限extensionof这些标准得到满足。这扩展了Yamazaki和Hiranouchi以前的工作。
We consider a productof elliptic curves over a finite extensionofwith a combination of good or split multiplicative reduction. We assume that at most one of the elliptic curves has supersingular reduction. Under these assumptions, we prove that the Albanese kernel ofis the direct sum of a finite group and a divisible group, extending work by Raskind and Spiess to cases that include supersingular phenomena. Our method involves studying the kernel of the cycle map. We give specific criteria that guarantee this map is injective for every. When all curves have good ordinary reduction, we show that it suffices to extend to a specific finite extensionoffor these criteria to be satisfied. This extends previous work by Yamazaki and Hiranouchi.