超奇异约简情况下的Selmer群

Pub Date : 2020-12-01 DOI:10.3836/tjm/1502179319
Antonio Lei, R. Sujatha
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引用次数: 10

摘要

设p是一个固定的奇素数。设E是定义在数域F上的一条椭圆曲线,在p以上的所有素数上都有良好的超奇异约化。我们研究了F的分环zp扩展上的经典Selmer群和正/负Selmer群。特别地,我们给出了这些Selmer群不包含有限指数的非平凡子模的充分条件。更进一步,当p在F中完全分裂时,我们计算了F的所有zp扩展的复合上的加/减Selmer群的欧拉特征。
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On Selmer Groups in the Supersingular Reduction Case
Let p be a fixed odd prime. Let E be an elliptic curve defined over a number field F with good supersingular reduction at all primes above p. We study both the classical and plus/minus Selmer groups over the cyclotomic Zp-extension of F . In particular, we give sufficient conditions for these Selmer groups to not contain a non-trivial sub-module of finite index. Furthermore, when p splits completely in F , we calculate the Euler characteristics of the plus/minus Selmer groups over the compositum of all Zp-extensions of F when they are defined.
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