Mazur's Growth Number Conjecture in the Rank One Case

2025/04/14 by Kundu, Debanjana, Lei, Antonio · 2 citations
#FOS: Mathematics #Number Theory (math.NT)

paper · doi:10.48550/arxiv.2504.10761

Abstract

Let p≥ 5 be a prime number. Let E/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 E over K is non-zero, then Mazur's conjecture on the growth of Selmer coranks in the ℤ_p²-extension of K holds.

Cited by

• Structure of (Fine) Mordell--Weil Groups
• Mazur's growth number conjecture and congruences

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