论文标题
残留的超植物iwasawa理论超过二次假想领域
Residual Supersingular Iwasawa Theory over quadratic imaginary fields
论文作者
论文摘要
令P为奇数元素，让E为e椭圆形曲线，该曲线在二次假想场上完全分裂。假设e在p上方的素数上具有超顺降低。我们在这些设置中定义并研究了Z_p^2延伸的精细双签名残差组。我们证明，对于两条残留的异构椭圆形曲线，一个椭圆曲线的符号μ-invariants消失意味着另一个符号μ-invariants消失。最后，我们表明，Selmer组的Pontryagin双重二元组和双签名的Selmer群体没有针对这些扩展的非平凡的伪无效子模块。
Let p be an odd prime and let E be an elliptic curve defined over a quadratic imaginary field where p splits completely. Suppose E has supersingular reduction at primes above p. We define and study the fine double-signed residual Selmer groups in these settings for Z_p^2-extensions. We prove that for two residually isomorphic elliptic curves, the vanishing of the signed μ-invariants of one elliptic curve implies the vanishing of the signed μ-invariants of the other. Finally, we show that the Pontryagin dual of the Selmer group and the double-signed Selmer groups have no non-trivial pseudo-null submodules for these extensions.
