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arXiv · 2206.03679

Residual Supersingular Iwasawa Theory over quadratic imaginary fields

Parham Hamidi
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Abstract

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 {\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.

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Parham Hamidi. 2022-06-08. Residual Supersingular Iwasawa Theory over quadratic imaginary fields. https://arxiv.org/abs/2206.03679

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