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RESIDUAL SUPERSINGULAR IWASAWA THEORY OVER QUADRATIC IMAGINARY FIELDS

  • Parham Hamidi (Department of Mathematics The University of British Columbia)
  • Received : 2022.07.04
  • Accepted : 2023.01.26
  • Published : 2023.07.31
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Abstract

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 [17] to ℤ2p-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 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.

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Acknowledgement

The author would like to thank Sujatha Ramdorai for suggesting this problem and her encouragement. The author also wishes to thank the anonymous referee for the detailed comments and corrections that helped improve this article.

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