Bull. Korean Math. Soc. 2023; 60(4): 1035-1059
Online first article July 5, 2023 Printed July 31, 2023
https://doi.org/10.4134/BKMS.b220461
Copyright © The Korean Mathematical Society.
Parham Hamidi
Vancouver, BC
Let $ p $ be an odd prime. 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 $. Under appropriate hypotheses, we extend the results of \cite{SujFil} to $ \mathbb{Z}_p^{2} $-extensions. We define and study the fine double-signed residual Selmer groups in these settings. We prove that for two residually isomorphic elliptic curves, the vanishing of the signed $ \mu $-invariants of one elliptic curve implies the vanishing of the signed $ \mu $-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.
Keywords: Iwasawa theory, supersingular elliptic curves, Selmer groups
MSC numbers: Primary 11R23, 14H52
© 2022. The Korean Mathematical Society. Powered by INFOrang Co., Ltd