What question did this study set out to answer?

The research aims to explore the properties of the dual Selmer group of elliptic curves over specific extensions, particularly focusing on the implications of the Heegner hypothesis.

March 1, 2026Open Access

Topics in anticyclotomic Iwasawa theory

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DNDac-Nhan-Tam NguyenUniversity of British Columbia

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Implication

This thesis investigates the dual Selmer group of elliptic curves over anticyclotomic extensions, indicating significant findings on invariants.

Key Points

The research aims to explore the properties of the dual Selmer group of elliptic curves over specific extensions, particularly focusing on the implications of the Heegner hypothesis.
Examined anticyclotomic extensions of imaginary quadratic fields related to elliptic curves.
Used algebraic techniques to establish the non-existence of finite submodules in specific cases.
Extended existing results on the μ-invariant and λ-invariants using simpler methods.
Conducted an analysis of BDP p-adic L-functions in relation to congruences of modular forms.
Demonstrated the non-existence of non-zero finite submodules under certain conditions.
Established the vanishing of the μ-invariant for elliptic curves related to specific Heegner points.
Observed variations in λ-invariants for p-residually isomorphic elliptic curves.
Investigated the behavior of p-adic L-functions for congruent modular forms, contributing to the analytic side of the study.

Cite This Study

Dac-Nhan-Tam Nguyen (2026) studied this question.

synapsesocial.com/papers/69a3d887ec16d51705d2f6bd https://doi.org/10.14288/1.0451556

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Implication

This thesis investigates the dual Selmer group of elliptic curves over anticyclotomic extensions, indicating significant findings on invariants.

Topics in anticyclotomic Iwasawa theory

Discussion

Member takes

Implication

Key Points

Cite This Study

Topics in anticyclotomic Iwasawa theory

Discussion

Member takes

Implication

Key Points

Cite This Study

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