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September 24, 2025Open Access

Galois cohomology of elliptic curves over anticyclotomic extensions

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. (Fri,) studied this question.

synapsesocial.com/papers/68d6e16f8b2b6861e4c401bb https://doi.org/https://doi.org/10.48550/arxiv.2508.11835

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