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arXiv · 2504.10761

Mazur's Growth Number Conjecture in the Rank One Case

Debanjana Kundu·Antonio Lei
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Abstract

Let $p\geq 5$ be a prime number. Let $\mathsf{E}/\mathbb{Q}$ be an elliptic curve with good ordinary reduction at $p$. Let $K$ be an imaginary quadratic field where $p$ splits, and such that the generalized Heegner hypothesis holds. Under mild hypotheses, we show that if the $p$-adic height of the Heegner point of $\mathsf{E}$ over $K$ is non-zero, then Mazur's conjecture on the growth of Selmer coranks in the $\mathbb{Z}_p^2$-extension of $K$ holds.

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Debanjana Kundu, Antonio Lei. 2025-04-14. Mazur's Growth Number Conjecture in the Rank One Case. https://arxiv.org/abs/2504.10761

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