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September 24, 20250 citationsOpen Access

Galois cohomology of elliptic curves over anticyclotomic extensions

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DNDac-Nhan-Tam NguyenRSR. Sujatha

Key Points

  • The study demonstrates a comprehensive view of galois cohomology for elliptic curves over anticyclotomic extensions.
  • Findings include the analysis of the dual selmer group, which is critical in understanding elliptic curve behavior.
  • Iwasawa theory is employed to explore the relationships within the anticyclotomic z_p-extension framework.
  • New insights into elliptic curves over imaginary quadratic fields provide a robust foundation for future research.

Abstract

Let K be an imaginary quadratic field and p be an odd prime number. Let E/Q be an elliptic curve with good ordinary reduction at p. We study the Iwasawa theory of E over the anticyclotomic Zₚ-extension of K by adopting a unifying framework. We also study the Galois cohomology of the dual Selmer group of E over the unique Zₚ²-extension of K as well as over the anticyclotomic extension of K.

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Cite This Study

Nguyen et al. (2025) studied this question.

synapsesocial.com/papers/68d6e16f8b2b6861e4c401bbhttps://doi.org/10.48550/arxiv.2508.11835
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